Positivity in algebraic geometry:
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| Format: | Book |
| Language: | English |
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Berlin [u.a.]
Springer
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| Edition: | [Paperback-Ausg.] |
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| Online Access: | Inhaltsverzeichnis Klappentext |
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| adam_text | Contents
Notation and Conventions
Part Two: Positivity for Vector Bundles
Introduction to Part Two
6
6.1
6.1.A Definition and First Properties
6.1.B Cohomological Propei ties
6.1.G Criteria for Amplitude
6.1.D Metric Approaches to Positivity of Vector Bundles
6.2
6.2.A Twists by Q-Divisors
Ö.2.B
6.3
6.3.A Normal and Tangent Bundles
6.3.B Ample Cotangent Bundles and Hyperbolicity
6.3.C
6.3.D The Bundle Associated to a Branched Covering
6.3.E Direct Images of Canonical Bundles
6.3.F Some Constructions of Positive Vector Bundles
6.4
6.4.A Review of Semistability
6.4.B Semistability and Amplitude
Notes
7
7.1
7.1.
XII
7.1.B Theorem
7.1.C
7.2
7.2.A Statements and First Examples
7.2.B Proof of Connectedness of Degeneracy Loci
7.2.
7.2.D Variants and Extensions
7.3
7.3.A Vanishing Theorems of Griffiths and
7.3.B Generalizations
Notes
8
8.1
8.1.A Chern Classes for Q-Twisted Bundles
8.1.B Cone Classes
8.1.C Cone Classes for Q-Twists
8.2
8.2.A Positivity of Chern Classes
8.2.B Positivity of Cone Classes
8.3
8.4
8.4.A Positivity of Intersection Products
8.4.B Non-Emptiness of Degeneracy Loci
8.4.C Singularities of Hypersurfaces Along a Curve
Notes
Part Three: Multiplier Ideals and Their Applications
Introduction to Part Three
9
9.1
9.1.A Q-Divisors
9.1.B Normal Crossing Divisors and Log Resolutions
9.1.C The Kawamata-Viehweg Vanishing Theorem
9.2
9.2.A Definition of Multiplier Ideals
9.2.B First Properties
9.3
9.3.A Multiplier Ideals and Multiplicity
9.3.B Invariants Arising from Multiplier Ideals
9.3.C Monomial Ideals
9.3.D Analytic Construction of Multiplier Ideals
Contents
9.3.E
9.3.F
9.3.G Multiplier Ideals on Singular Varieties
9.4
9.4.A Local Vanishing for Multiplier Ideals
9.4.B The
9.4.C Vanishing on Singular Varieties
9.4.D Nadel s Theorem in the Analytic Setting
9.4.E
9.5
9.5.A Restrictions of Multiplier Ideals
9.5.B Subadditivity
9.5.C The Summation Theorem
9.5.D Multiplier Ideals in Families
9.5.E Coverings
9.6
9.6.A Integral Closure of Ideals
9.6.B Skoda s Theorem: Statements
9.6.C Skoda s Theorem: Proofs
9.6.D Variants
Notes
10
10.1
10.1.A Singularities of Projective Hypersurfaces
10.1.B Singularities of Theta Divisors
10.1.C A Criterion for Separation of Jets of Adjoint Series
10.2
10.3
10.4
10.4.A Fujita Conjecture and Angehrn-Siu Theorem
10.4.B Loci of Log-Canonical Singularities
10.4.C Proof of the Theorem of Angehrn and Siu
10.5
Notes
11
11.1
ll.l.A Complete Linear Series
ll.l.B Graded Systems of Ideals and Linear Series
11.2
11.2.A Local Statements
11.2.B Global Results
11.2.C Multiplicativity of Plurigenera
11.3
XIV
11.4 Fujita s Approximation Theorem..........................299
11.4.
11.4.B
11.4.C
11.5
Notes
References
Glossary of Notation
Index
Contents
Notation and Conventions 1:
Part One: Ample Line Bundles and Linear Series
Introduction to Part One 1:
1
1.1
l.l.A Divisors and Line Bundles
1.1.
1.1.
1.1.
1.2
1.2.A Cohomological Properties 1:
1.2.B Numerical Properties 1:
1.2.C Metric Characterizations of Amplitude 1:
1.3
1.3.A Definitions for Q-Divisors
1.3.B R-Divisors and Their Amplitude 1:
1.4
1.4.A Definitions and Formal Properties i:
1.4.B Kleiman s Theorem
1.4.C Cones
1.4.D Pujita s Vanishing Theorem
1.5
1.5.A Ruled Surfaces 1:
1.5.B Products of Curves 1:
1.5.C Abelian Varieties i:
1.5.D Other Varieties i:
1.5.E Local Structure of the
XVI
1.5.F
1.6
1.6.A Global Results i:
1.6.B Mixed Multiplicities 1:
1.7
1.8
1.8.A Definitions, Formal Properties, and Variants i:
1.8.B Regularity and Complexity 1:
1.8.C Regularity Bounds 1:
1.8.D Syzygies of Algebraic Varieties
Notes 1:
2
2.1
2.1.A Basic Definitions
2.1.B Semiample Line Bundles 1:
2.1.C Iitaka Fibration
2.2
2.2.A Basic Properties of Big Divisors 1:
2.2.B
2.2.C Volume of a Big Divisor 1:
2.3
2.3.A Zariski s Construction i:
2.3.B Cutkosky s Construction 1:
2.3.
2.3.D The Theorem of
2.3.E Zariski Decompositions i:
2.4
2.4.A Graded Linear Series 1:
2.4.B Graded Families of Ideals i:
Notes i:
3
3.1
3.1.
3.1.B The Theorem on
3.1.C Hard Lefschetz Theorem 1:
3.2
3.2.A Barth s Theorem 1:
3.2.B Hartshorne s Conjectures 1:
3.3
3.3.A
3.3.B Theorem of Fulton and
3.3.C Grothendieck s Connectedness Theorem 1:
3.4
3.4.A Singularities of Mappings 1:
Contents of Volume I XVII
3.4.B Zak s Theorems 1:
3.4.C Zariski s Problem i:
3.5
3.5.A Homogeneous Varieties 1:
3.5.B Higher Connectivity 1:
Notes i:
Vanishing Theorems 1:
4.1
4.1.
4.1.B Covering Lemmas 1:
4.2
4.3
4.3.A Statement and Proof of the Theorem 1:
4.3.B Some Applications 1:
4.4
Notes i:
Local Positivity 1:
5.1
5.2
5.2.A Background and Statements 1:
5.2.B Multiplicities of Divisors in Families 1:
5.2.C Proof of Theorem
5.3
5.3.A Period Lengths and Seshadri Constants i:
5.3.B Proof of Theorem
5.3.C Complements 1:
5.4
5.4.A Definition and Formal Properties of the s-Invariant i:
5.4.B Complexity Bounds 1:
Notes 1:
Appendices
A Projective Bundles 1:
B Cohomology and Complexes 1:
B.I Cohomology
B.2 Complexes
References i:
Glossary of Notation 1:
Index i:
LAZARSFELD
Positivity in Algebraic Geometry n
This two-volume book on Positivity in Algebraic Geometry
contains a contemporary account of a body of work in com¬
plex algebraic geometry loosely centered around the theme
of positivity. Topics in Volume I include ample line bundles
and linear series on a projective variety, the classical theo¬
rems of Lefschetz and
vanishing theorems, and local positivity. Volume II begins
with a survey of positivity for vector bundles, and moves on
to a systematic development of the theory of multiplier ideals
and their applications. At least a third of the book is devoted
to concrete examples, applications, and pointers to further
developments. Most of the material in the present Volume II
has not previously appeared in book form, and substantial
parts are worked out here in detail for the first time. Both
volumes are also available as hardcover editions as
and
Grenzgebiete.
|
| any_adam_object | 1 |
| author | Lazarsfeld, Robert 1953- |
| author_GND | (DE-588)102154279 |
| author_facet | Lazarsfeld, Robert 1953- |
| author_role | aut |
| author_sort | Lazarsfeld, Robert 1953- |
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| discipline | Mathematik |
| edition | [Paperback-Ausg.] |
| format | Book |
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| spelling | Lazarsfeld, Robert 1953- Verfasser (DE-588)102154279 aut Positivity in algebraic geometry Robert Lazarsfeld [Paperback-Ausg.] Berlin [u.a.] Springer txt rdacontent n rdamedia nc rdacarrier Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Positive Definitheit (DE-588)4382343-9 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 s Positive Definitheit (DE-588)4382343-9 s DE-604 Digitalisierung UBRegensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012876678&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012876678&sequence=000002&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Lazarsfeld, Robert 1953- Positivity in algebraic geometry Algebraische Geometrie (DE-588)4001161-6 gnd Positive Definitheit (DE-588)4382343-9 gnd |
| subject_GND | (DE-588)4001161-6 (DE-588)4382343-9 |
| title | Positivity in algebraic geometry |
| title_auth | Positivity in algebraic geometry |
| title_exact_search | Positivity in algebraic geometry |
| title_full | Positivity in algebraic geometry Robert Lazarsfeld |
| title_fullStr | Positivity in algebraic geometry Robert Lazarsfeld |
| title_full_unstemmed | Positivity in algebraic geometry Robert Lazarsfeld |
| title_short | Positivity in algebraic geometry |
| title_sort | positivity in algebraic geometry |
| topic | Algebraische Geometrie (DE-588)4001161-6 gnd Positive Definitheit (DE-588)4382343-9 gnd |
| topic_facet | Algebraische Geometrie Positive Definitheit |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012876678&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012876678&sequence=000002&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT lazarsfeldrobert positivityinalgebraicgeometry |