Symplectic 4-manifolds and algebraic surfaces: lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 2 - 10, 2003
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2008
|
| Series: | Lecture notes in mathematics
1938 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 345 S. graph. Darst. |
| ISBN: | 9783540782780 3540782788 |
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MARC
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| 100 | 1 | |a Auroux, Denis |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Symplectic 4-manifolds and algebraic surfaces |b lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 2 - 10, 2003 |c Denis Auroux ... Ed.: Fabrizio Catanese ... |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2008 | |
| 300 | |a XIII, 345 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1938 | |
| 650 | 4 | |a Surfaces algébriques - Congrès | |
| 650 | 4 | |a Variétés (Mathématiques) - Congrès | |
| 650 | 4 | |a Variétés symplectiques - Congrès | |
| 650 | 4 | |a Manifolds (Mathematics) |v Congresses | |
| 650 | 4 | |a Surfaces, Algebraic |v Congresses | |
| 650 | 4 | |a Symplectic manifolds |v Congresses | |
| 650 | 0 | 7 | |a Symplektische Mannigfaltigkeit |0 (DE-588)4290704-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algebraische Fläche |0 (DE-588)4195660-6 |2 gnd |9 rswk-swf |
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| 830 | 0 | |a Lecture notes in mathematics |v 1938 |w (DE-604)BV000676446 |9 1938 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-016479059 | ||
Record in the Search Index
| _version_ | 1804137619607519232 |
|---|---|
| adam_text | Contents
Lefschetz
Pencils, Branched
Covers
and Symplectic Invariants
Denis
Auroux and Ivan Smith
..................................... 1
1
Introduction and Background
................................... 1
1.1
Symplectic Manifolds
...................................... 1
1.2
Almost-Complex Structures
................................ 3
1.3
Pseudo-
Holomorphic Curves and Gromov-Witten Invariants
.... 5
1.4
Lagrangian
Floer Homology
................................ 6
1.5
The Topology of Symplectic Four-Manifolds
.................. 9
2
Symplectic Lefschetz Fibrations
................................. 10
2.1
Fibrations and Monodromy
................................. 10
2.2
Approximately Holomorphic Geometry
....................... 17
3
Symplectic Branched Covers of CP2
............................. 22
3.1
Symplectic Branched Covers
................................ 22
3.2
Monodromy Invariants for Branched Covers of CP2
............ 26
3.3
Fundamental Groups of Branch Curve Complements
........... 30
3.4
Symplectic
Isotopy
and Non-Isotopy
......................... 33
4
Symplectic Surfaces from Symmetric Products
.................... 35
4.1
Symmetric Products
....................................... 35
4.2 Taubes
Theorem
.......................................... 39
5
Fukaya Categories and Lefschetz Fibrations
....................... 42
5.1
Matching Paths and Lagrangian Spheres
..................... 43
5.2
Fukaya Categories of Vanishing Cycles
....................... 44
5.3
Applications to Mirror Symmetry
........................... 48
References
...................................................... 50
Differentiable and Deformation Type of Algebraic Surfaces,
Real and Symplectic Structures
Fabrizio Catanese................................................ 55
1
Introduction
.................................................. 55
2
Lecture
1:
Projective
and
Kahler
Manifolds, the
Enriques
Classification, Construction Techniques
........................... 57
2.1
Projective
Manifolds,
Kahler
and Symplectic Structures
........ 57
X
Contents
2.2 The Birational
Equivalence of Algebraic Varieties
............. 63
2.3
The
Enriques
Classification: An Outline
...................... 65
2.4
Some Constructions of
Projective
Varieties
................... 66
3
Lecture
2:
Surfaces of General Type and Their Canonical Models:
Deformation Equivalence and Singularities
........................ 70
3.1
Rational Double Points
.................................... 70
3.2
Canonical Models of Surfaces of General Type
................ 74
3.3
Deformation Equivalence of Surfaces
......................... 82
3.4
Isolated Singularities, Simultaneous Resolution
................ 85
4
Lecture
3:
Deformation and Diffeomorphism, Canonical Symplectic
Structure for Surfaces of General Type
........................... 91
4.1
Deformation Implies Diffeomorphism
........................ 92
4.2
Symplectic Approximations of
Projective
Varieties with Isolated
Singularities
.............................................. 93
4.3
Canonical Symplectic Structure for Varieties with Ample
Canonical Class and Canonical Symplectic Structure
for Surfaces of General Type
................................ 95
4.4
Degenerations Preserving the Canonical Symplectic Structure
... 96
5
Lecture
4:
Irrational Pencils, Orbifold Fundamental Groups,
and Surfaces Isogenous to a Product
............................. 98
5.1
Theorem of Castelnuovo-De
Franchis,
Irrational Pencils
and the Orbifold Fundamental Group
........................ 99
5.2
Varieties Isogenous to a Product
............................105
5.3
Complex Conjugation and Real Structures
....................108
5.4
Beauville Surfaces
.........................................114
6
Lecture
5:
Lefschetz Pencils, Braid and Mapping Class Groups,
and Diffeomorphism of ABC-Surfaces
............................116
6.1
Surgeries
.................................................116
6.2
Braid and Mapping Class Groups
...........................119
6.3
Lefschetz Pencils and Lefschetz Fibrations
....................125
6.4
Simply Connected Algebraic Surfaces: Topology Versus
Differential Topology
......................................130
6.5
ABC Surfaces
.............................................134
7
Epilogue: Deformation, Diffeomorphism and Symplectomorphism
Type of Surfaces of General Type
...............................140
7.1
Deformations in the Large of ABC Surfaces
...................141
7.2
Manetta
Surfaces
..........................................145
7.3
Deformation and Canonical Symplectomorphism
..............152
7.4
Braid
Monodramy
and Chisini Problem
.....................154
References
......................................................159
Smoothings of Singularities and Deformation Types
of Surfaces
Marco Manetti
...................................................169
1
Introduction
..................................................169
Contents
XI
2 Deformation
Equivalence
of Surfaces
.............................174
2.1
Rational Double Points
....................................174
2.2
Quotient Singularities
......................................178
2.3
RDP-Deformation Equivalence
..............................181
2.4
Relative Canonical Model
..................................182
2.5
Automorphisms of Canonical Models
........................183
2.6
The Kodaira-Spencer Map
.................................184
3
Moduli Space for Canonical Surfaces
.............................187
3.1
Gieseker s Theorem
........................................188
3.2
Constructing Connected Components: Some Strategies
.........189
3.3
Outline of Proof of Gieseker Theorem
.......................190
4
Smoothings of Normal Surface Singularities
.......................194
4.1
The Link of an Isolated Singularity
..........................194
4.2
The Milnor Fibre
..........................................196
4.3
Q-Gorenstein Singularities and Smoothings
...................197
4.4
Т
-Deformation Equivalence of Surfaces
.......................201
4.5
A Non
Trivial Example of T-Deformation Equivalence
.........203
5
Double and Multidouble Covers of Normal Surfaces
................204
5.1
Flat Abelian Covers
.......................................204
5.2
Flat Double Covers
........................................205
5.3
Automorphisms of Generic Flat Double Covers
................207
5.4
Example: Automorphisms of Simple Iterated Double Covers
.... 209
5.5
Flat Multidouble Covers
...................................210
6
Stability Criteria for Flat Double Covers
.........................213
6.1
Restricted Natural Deformations of Double Covers
............214
6.2
Openess of N(a, b,c)
.......................................217
6.3
RDP-Degenerations of Double Covers
........................218
6.4
RDP-Degenerations of
P1 x
P1
..............................221
6.5
Proof of Theorem
6.1......................................222
6.6
Moduli of Simple Iterated Double Covers
.....................223
References
......................................................225
Lectures on Four-Dimensional
Dehn
Twists
Paul
Seidel......................................................231
1
Introduction
..................................................231
2
Definition and First Properties
..................................235
3
Floer
and Quantum Homology
..................................249
4
Pseudo-Holomorphic Sections and Curvature
......................259
References
......................................................265
Lectures on Pseudo-Holomorphic Curves and the Symplectic
Isotopy
Problem
Bernd Siebert
and Gang
Tian
.....................................269
1
Introduction
..................................................269
2
Pseudo-Holomorphic Curves
....................................270
XII Contents
2.1
Almost
Complex
and Symplectic Geometry
...................270
2.2
Basic Properties of Pseudo-Holomorphic Curves
...............272
2.3
Moduli Spaces
............................................273
2.4
Applications
..............................................276
2.5
Pseudo-
Analytic Inequalities
................................279
3
Unobstructedness I: Smooth and Nodal Curves
....................281
3.1
Preliminaries on the 9-Equation
.............................281
3.2
The Normal d-Operator
....................................282
3.3
Immersed Curves
..........................................286
3.4
Smoothings of Nodal Curves
................................287
4
The Theorem of Micallef and White
.............................288
4.1
Statement of Theorem
.....................................288
4.2
The Case of Tacnodes
......................................289
4.3
The General Case
.........................................291
5
Unobstructedness II: The
Integrable
Case
........................292
5.1
Motivation
...............................................292
5.2
Special Covers
............................................292
5.3
Description of the Deformation Space
........................294
5.4
The Holomorphic Normal Sheaf
.............................296
5.5
Computation of the Linearization
...........................299
5.6
A Vanishing Theorem
......................................300
5.7
The Unobstructedness Theorem
.............................301
6
Application to Symplectic Topology in Dimension Four
.............302
6.1
Monodromy Representations
-
Hurwitz Equivalence
...........303
6.2
Hyperelliptic Lefschetz Fibrations
...........................304
6.3
Braid Monodromy and the Structure of Hyperelliptic Lefschetz
Fibrations
................................................307
6.4
Symplectic Noether-Horikawa Surfaces
.......................309
7
The ^-Compactness Theorem for Pseudo-Holomorphic Curves
.....311
7.1
Statement of Theorem and Conventions
......................311
7.2
The Monotonicity Formula for Pseudo-Holomorphic Maps
......312
7.3
A Removable Singularities Theorem
.........................315
7.4
Proof of the Theorem
......................................316
8
Second Variation of the Oj-Equation and Applications
.............320
8.1
Comparisons of First and Second Variations
..................321
8.2
Moduli Spaces of Pseudo-Holomorphic Curves with Prescribed
Singularities
..............................................323
8.3
The Locus of Constant Deficiency
...........................324
8.4
Second Variation at Ordinary Cusps
.........................328
Contents XIII
9 The
Isotopy
Theorem
..........................................332
9.1
Statement of Theorem and Discussion
.......................332
9.2
Pseudo-Holomorphic Techniques for the
Isotopy
Problem
.......333
9.3
The
Isotopy
Lemma
.......................................334
9.4
Sketch of Proof
...........................................336
References
......................................................339
List of Participants
............................................343
|
| adam_txt |
Contents
Lefschetz
Pencils, Branched
Covers
and Symplectic Invariants
Denis
Auroux and Ivan Smith
. 1
1
Introduction and Background
. 1
1.1
Symplectic Manifolds
. 1
1.2
Almost-Complex Structures
. 3
1.3
Pseudo-
Holomorphic Curves and Gromov-Witten Invariants
. 5
1.4
Lagrangian
Floer Homology
. 6
1.5
The Topology of Symplectic Four-Manifolds
. 9
2
Symplectic Lefschetz Fibrations
. 10
2.1
Fibrations and Monodromy
. 10
2.2
Approximately Holomorphic Geometry
. 17
3
Symplectic Branched Covers of CP2
. 22
3.1
Symplectic Branched Covers
. 22
3.2
Monodromy Invariants for Branched Covers of CP2
. 26
3.3
Fundamental Groups of Branch Curve Complements
. 30
3.4
Symplectic
Isotopy
and Non-Isotopy
. 33
4
Symplectic Surfaces from Symmetric Products
. 35
4.1
Symmetric Products
. 35
4.2 Taubes'
Theorem
. 39
5
Fukaya Categories and Lefschetz Fibrations
. 42
5.1
Matching Paths and Lagrangian Spheres
. 43
5.2
Fukaya Categories of Vanishing Cycles
. 44
5.3
Applications to Mirror Symmetry
. 48
References
. 50
Differentiable and Deformation Type of Algebraic Surfaces,
Real and Symplectic Structures
Fabrizio Catanese. 55
1
Introduction
. 55
2
Lecture
1:
Projective
and
Kahler
Manifolds, the
Enriques
Classification, Construction Techniques
. 57
2.1
Projective
Manifolds,
Kahler
and Symplectic Structures
. 57
X
Contents
2.2 The Birational
Equivalence of Algebraic Varieties
. 63
2.3
The
Enriques
Classification: An Outline
. 65
2.4
Some Constructions of
Projective
Varieties
. 66
3
Lecture
2:
Surfaces of General Type and Their Canonical Models:
Deformation Equivalence and Singularities
. 70
3.1
Rational Double Points
. 70
3.2
Canonical Models of Surfaces of General Type
. 74
3.3
Deformation Equivalence of Surfaces
. 82
3.4
Isolated Singularities, Simultaneous Resolution
. 85
4
Lecture
3:
Deformation and Diffeomorphism, Canonical Symplectic
Structure for Surfaces of General Type
. 91
4.1
Deformation Implies Diffeomorphism
. 92
4.2
Symplectic Approximations of
Projective
Varieties with Isolated
Singularities
. 93
4.3
Canonical Symplectic Structure for Varieties with Ample
Canonical Class and Canonical Symplectic Structure
for Surfaces of General Type
. 95
4.4
Degenerations Preserving the Canonical Symplectic Structure
. 96
5
Lecture
4:
Irrational Pencils, Orbifold Fundamental Groups,
and Surfaces Isogenous to a Product
. 98
5.1
Theorem of Castelnuovo-De
Franchis,
Irrational Pencils
and the Orbifold Fundamental Group
. 99
5.2
Varieties Isogenous to a Product
.105
5.3
Complex Conjugation and Real Structures
.108
5.4
Beauville Surfaces
.114
6
Lecture
5:
Lefschetz Pencils, Braid and Mapping Class Groups,
and Diffeomorphism of ABC-Surfaces
.116
6.1
Surgeries
.116
6.2
Braid and Mapping Class Groups
.119
6.3
Lefschetz Pencils and Lefschetz Fibrations
.125
6.4
Simply Connected Algebraic Surfaces: Topology Versus
Differential Topology
.130
6.5
ABC Surfaces
.134
7
Epilogue: Deformation, Diffeomorphism and Symplectomorphism
Type of Surfaces of General Type
.140
7.1
Deformations in the Large of ABC Surfaces
.141
7.2
Manetta
Surfaces
.145
7.3
Deformation and Canonical Symplectomorphism
.152
7.4
Braid
Monodramy
and Chisini' Problem
.154
References
.159
Smoothings of Singularities and Deformation Types
of Surfaces
Marco Manetti
.169
1
Introduction
.169
Contents
XI
2 Deformation
Equivalence
of Surfaces
.174
2.1
Rational Double Points
.174
2.2
Quotient Singularities
.178
2.3
RDP-Deformation Equivalence
.181
2.4
Relative Canonical Model
.182
2.5
Automorphisms of Canonical Models
.183
2.6
The Kodaira-Spencer Map
.184
3
Moduli Space for Canonical Surfaces
.187
3.1
Gieseker's Theorem
.188
3.2
Constructing Connected Components: Some Strategies
.189
3.3
Outline of Proof of Gieseker Theorem
.190
4
Smoothings of Normal Surface Singularities
.194
4.1
The Link of an Isolated Singularity
.194
4.2
The Milnor Fibre
.196
4.3
Q-Gorenstein Singularities and Smoothings
.197
4.4
Т
-Deformation Equivalence of Surfaces
.201
4.5
A Non
Trivial Example of T-Deformation Equivalence
.203
5
Double and Multidouble Covers of Normal Surfaces
.204
5.1
Flat Abelian Covers
.204
5.2
Flat Double Covers
.205
5.3
Automorphisms of Generic Flat Double Covers
.207
5.4
Example: Automorphisms of Simple Iterated Double Covers
. 209
5.5
Flat Multidouble Covers
.210
6
Stability Criteria for Flat Double Covers
.213
6.1
Restricted Natural Deformations of Double Covers
.214
6.2
Openess of N(a, b,c)
.217
6.3
RDP-Degenerations of Double Covers
.218
6.4
RDP-Degenerations of
P1 x
P1
.221
6.5
Proof of Theorem
6.1.222
6.6
Moduli of Simple Iterated Double Covers
.223
References
.225
Lectures on Four-Dimensional
Dehn
Twists
Paul
Seidel.231
1
Introduction
.231
2
Definition and First Properties
.235
3
Floer
and Quantum Homology
.249
4
Pseudo-Holomorphic Sections and Curvature
.259
References
.265
Lectures on Pseudo-Holomorphic Curves and the Symplectic
Isotopy
Problem
Bernd Siebert
and Gang
Tian
.269
1
Introduction
.269
2
Pseudo-Holomorphic Curves
.270
XII Contents
2.1
Almost
Complex
and Symplectic Geometry
.270
2.2
Basic Properties of Pseudo-Holomorphic Curves
.272
2.3
Moduli Spaces
.273
2.4
Applications
.276
2.5
Pseudo-
Analytic Inequalities
.279
3
Unobstructedness I: Smooth and Nodal Curves
.281
3.1
Preliminaries on the 9-Equation
.281
3.2
The Normal d-Operator
.282
3.3
Immersed Curves
.286
3.4
Smoothings of Nodal Curves
.287
4
The Theorem of Micallef and White
.288
4.1
Statement of Theorem
.288
4.2
The Case of Tacnodes
.289
4.3
The General Case
.291
5
Unobstructedness II: The
Integrable
Case
.292
5.1
Motivation
.292
5.2
Special Covers
.292
5.3
Description of the Deformation Space
.294
5.4
The Holomorphic Normal Sheaf
.296
5.5
Computation of the Linearization
.299
5.6
A Vanishing Theorem
.300
5.7
The Unobstructedness Theorem
.301
6
Application to Symplectic Topology in Dimension Four
.302
6.1
Monodromy Representations
-
Hurwitz Equivalence
.303
6.2
Hyperelliptic Lefschetz Fibrations
.304
6.3
Braid Monodromy and the Structure of Hyperelliptic Lefschetz
Fibrations
.307
6.4
Symplectic Noether-Horikawa Surfaces
.309
7
The ^-Compactness Theorem for Pseudo-Holomorphic Curves
.311
7.1
Statement of Theorem and Conventions
.311
7.2
The Monotonicity Formula for Pseudo-Holomorphic Maps
.312
7.3
A Removable Singularities Theorem
.315
7.4
Proof of the Theorem
.316
8
Second Variation of the Oj-Equation and Applications
.320
8.1
Comparisons of First and Second Variations
.321
8.2
Moduli Spaces of Pseudo-Holomorphic Curves with Prescribed
Singularities
.323
8.3
The Locus of Constant Deficiency
.324
8.4
Second Variation at Ordinary Cusps
.328
Contents XIII
9 The
Isotopy
Theorem
.332
9.1
Statement of Theorem and Discussion
.332
9.2
Pseudo-Holomorphic Techniques for the
Isotopy
Problem
.333
9.3
The
Isotopy
Lemma
.334
9.4
Sketch of Proof
.336
References
.339
List of Participants
.343 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Auroux, Denis Catanese, Fabrizio 1950- |
| author_GND | (DE-588)113784872 |
| author_facet | Auroux, Denis Catanese, Fabrizio 1950- |
| author_role | aut aut |
| author_sort | Auroux, Denis |
| author_variant | d a da f c fc |
| building | Verbundindex |
| bvnumber | BV023294500 |
| callnumber-first | Q - Science |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 850 |
| classification_tum | MAT 533f MAT 146f |
| ctrlnum | (OCoLC)213479402 (DE-599)DNB98721859X |
| dewey-full | 516.3/52 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/52 |
| dewey-search | 516.3/52 |
| dewey-sort | 3516.3 252 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| genre | (DE-588)1071861417 Konferenzschrift 2003 Cetraro gnd-content |
| genre_facet | Konferenzschrift 2003 Cetraro |
| id | DE-604.BV023294500 |
| illustrated | Illustrated |
| index_date | 2024-07-02T20:44:22Z |
| indexdate | 2024-07-09T21:15:11Z |
| institution | BVB |
| institution_GND | (DE-588)1025933-8 |
| isbn | 9783540782780 3540782788 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016479059 |
| oclc_num | 213479402 |
| open_access_boolean | |
| owner | DE-706 DE-824 DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-83 DE-11 DE-188 |
| owner_facet | DE-706 DE-824 DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-83 DE-11 DE-188 |
| physical | XIII, 345 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Auroux, Denis Verfasser aut Symplectic 4-manifolds and algebraic surfaces lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 2 - 10, 2003 Denis Auroux ... Ed.: Fabrizio Catanese ... Berlin [u.a.] Springer 2008 XIII, 345 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1938 Surfaces algébriques - Congrès Variétés (Mathématiques) - Congrès Variétés symplectiques - Congrès Manifolds (Mathematics) Congresses Surfaces, Algebraic Congresses Symplectic manifolds Congresses Symplektische Mannigfaltigkeit (DE-588)4290704-4 gnd rswk-swf Algebraische Fläche (DE-588)4195660-6 gnd rswk-swf Dimension 4 (DE-588)4338676-3 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 2003 Cetraro gnd-content Symplektische Mannigfaltigkeit (DE-588)4290704-4 s Dimension 4 (DE-588)4338676-3 s Algebraische Fläche (DE-588)4195660-6 s DE-604 Catanese, Fabrizio 1950- Verfasser (DE-588)113784872 aut Centro Internazionale Matematico Estivo Sonstige (DE-588)1025933-8 oth Lecture notes in mathematics 1938 (DE-604)BV000676446 1938 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016479059&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Auroux, Denis Catanese, Fabrizio 1950- Symplectic 4-manifolds and algebraic surfaces lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 2 - 10, 2003 Lecture notes in mathematics Surfaces algébriques - Congrès Variétés (Mathématiques) - Congrès Variétés symplectiques - Congrès Manifolds (Mathematics) Congresses Surfaces, Algebraic Congresses Symplectic manifolds Congresses Symplektische Mannigfaltigkeit (DE-588)4290704-4 gnd Algebraische Fläche (DE-588)4195660-6 gnd Dimension 4 (DE-588)4338676-3 gnd |
| subject_GND | (DE-588)4290704-4 (DE-588)4195660-6 (DE-588)4338676-3 (DE-588)1071861417 |
| title | Symplectic 4-manifolds and algebraic surfaces lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 2 - 10, 2003 |
| title_auth | Symplectic 4-manifolds and algebraic surfaces lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 2 - 10, 2003 |
| title_exact_search | Symplectic 4-manifolds and algebraic surfaces lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 2 - 10, 2003 |
| title_exact_search_txtP | Symplectic 4-manifolds and algebraic surfaces lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 2 - 10, 2003 |
| title_full | Symplectic 4-manifolds and algebraic surfaces lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 2 - 10, 2003 Denis Auroux ... Ed.: Fabrizio Catanese ... |
| title_fullStr | Symplectic 4-manifolds and algebraic surfaces lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 2 - 10, 2003 Denis Auroux ... Ed.: Fabrizio Catanese ... |
| title_full_unstemmed | Symplectic 4-manifolds and algebraic surfaces lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 2 - 10, 2003 Denis Auroux ... Ed.: Fabrizio Catanese ... |
| title_short | Symplectic 4-manifolds and algebraic surfaces |
| title_sort | symplectic 4 manifolds and algebraic surfaces lectures given at the c i m e summer school held in cetraro italy september 2 10 2003 |
| title_sub | lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 2 - 10, 2003 |
| topic | Surfaces algébriques - Congrès Variétés (Mathématiques) - Congrès Variétés symplectiques - Congrès Manifolds (Mathematics) Congresses Surfaces, Algebraic Congresses Symplectic manifolds Congresses Symplektische Mannigfaltigkeit (DE-588)4290704-4 gnd Algebraische Fläche (DE-588)4195660-6 gnd Dimension 4 (DE-588)4338676-3 gnd |
| topic_facet | Surfaces algébriques - Congrès Variétés (Mathématiques) - Congrès Variétés symplectiques - Congrès Manifolds (Mathematics) Congresses Surfaces, Algebraic Congresses Symplectic manifolds Congresses Symplektische Mannigfaltigkeit Algebraische Fläche Dimension 4 Konferenzschrift 2003 Cetraro |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016479059&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
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