Complex curves in almost complex manifolds and meromorphic hulls:
Gespeichert in:
| Hauptverfasser: | , |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Bochum
Inst. für Mathematik, Ruhr-Univ.
1999
|
| Schriftenreihe: | Graduiertenkolleg Geometrie und Mathematische Physik <Bochum>: Schriftenreihe des Graduiertenkollegs Geometrie und Mathematische Physik
36 |
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| Beschreibung: | 186 S. |
Internformat
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| 245 | 1 | 0 | |a Complex curves in almost complex manifolds and meromorphic hulls |c Sergei Ivashkovich ; Vsevolod Shevchishin |
| 264 | 1 | |a Bochum |b Inst. für Mathematik, Ruhr-Univ. |c 1999 | |
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Datensatz im Suchindex
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| adam_text |
COMPLEX CURVES IN ALMOST COMPLEX
MANIFOLDS AND MEROMORPHIC HULLS
Sergei IVASHKOVICH Vsevolod SHEVCHISHIN
Preface
Chapter I. Local Properties of Complex Curves.
Lecture 1. Complex Curves in Almost Complex Manifolds. . . . pp. 1 12
1.1. Almost Complex Manifolds, Hermitian Metrics, As¬
sociated (l,l) Forms. 1.2. Existence of Calibrating and
Tame Structures. 1.3. Almost Complex Submanifold,
Complex Curves, Energy and Area. 1.4. Symplectic Sur¬
faces. 1.5. Adjunction Formula for Immersed Symplectic
Surfaces.
Appendix I. Chern Class and Riemann Roch Formula pp. 13 14
AI.l. First Chern Class of a Complex Bundle. AI.2. Rie
manu Roch Formula and Index of d Type Operators.
Lecture 2. Local Existence of Curves pp. 15 21
2.1. Sobolev Imbeddings, Cauchy Green Operators, Cal
deron Zygmund Inequality. 2.2. Local Existence of Com¬
plex Curves in Nonintegrable Structures. 2.3. General¬
ized Calderon Zyginund Inequality. 2.4. First A priori Es¬
timate. 2.5. Convergency outside of Finite Set of Points.
Lecture 3. Positivity of Intersections of Complex Curves pp. 22 37
3.1. Unique Continuation Lemma. 3.2. Inversion oidj+R
and £fcp Topologies. 3.3. Perturbing Cusps of Complex
Curves. 3.4. Primitivity. 3.5. Positivity of Intersections.
Appendix II. The Bennequin Index and Genus Formula pp. 38 43
AII.l. Bennequin Index of a Cusp. All.2. Proof of Ad¬
junction Formula. AII.3. A Matching Structures Lemma.
Chapter II. Compactness Theorem.
Lecture 4. Space of Stable Curves and Maps pp. 46 66
4.1. Stable Maps and Gromov Topology. 4.2. Fenchel
Nielsen Coordinates on the Space of Nodal Curves. 4.3.
Complex Structure on the Space Tr. 4.4. Invariant De¬
scription of the Complex Structure on Tp. 4.5. Example:
Degeneration to a Half cubic Parabola on the Language
of Stable Curves.
Lecture 5. Gromov Compactness Theorem pp. 67 84
5.1. Second A priori Estimate. 5.2. Removal of Singular¬
ities. 5.3. Compactness for the Curves with Free Bound¬
ary.
ii
Appendix III. Compactness with Boundary Conditions pp. 85 110
A3.1. Curves with Bondary on Totally Real Submani
folds. A3.2. A priori Estimates near a Totally Real
Boundary. A3.3. Long Strips and the Second A priori
Estimate. A3.4. Gromov Compactness for Curves with
Totally Real Boundary Conditions. A3.5. Attaching an
Analytic Disk to a Lagrangian Submanifold in C".
Chapter III. Global Properties and Moduli Spaces.
Lecture 6. First Variation of dj Equation pp. 111 122
6.1. Symmetric Connections. 6.2. Definition of Dnj Ope¬
rator. 6.3. d type Operators. 6.4. Holomorphic Structure
on the Induced Bundle.
Lecture 7. Fredholm Properties of Gromov Operator pp. 123 129
7.1. Generalized Normal Bundle. 7.2. Surjectivity of DuJ
operator. 7.3. Tangent Space to the Moduli Space. 7.4.
Reparameterizations.
Lecture 8. Transversality. pp. 130 144
8.1. Moduli Space of Nonparameterized Complex Curves.
8.2. Transversal maps. 8.3. Components of the Moduli
Space. 8.4. Moduli of Parameterized Curves. 8.5. Gro¬
mov Nonsqueezing Theorem. 8.6. Exeptional Spheres in
Symplectic 4 Manifolds.
Chapter IV. Envelopes of Meromorphy.
Lecture 9. Deformation of Noncompact Curves pp. 147 159
9.1. Banach Analytic Sets. 9.2. Solution of a Cousin type
Problem. 9.3. Case of a Stein Curve. 9.4. Degeneration
to a Node. 9.5. Banach Analytic Structure of the Stable
Neighborhoods. 9.6. Drawing Families of Curves.
Lecture 10. Envelopes of Meromorphy of Two Spheres pp. 160 168
10.1. Continuity Principle relative to the Kahler Spaces.
10.2. Proof of the Continuity Principle. 10.3. Construc¬
tion of Envelopes I. 10.4. Construction of Envelopes
II. 10.5. Examples. 10.6. Rigidity of Symplectic Imbed
dings.
Appendix IV. Complex Points and Stein Neighborhods. . . . pp. 169 172
A4.1. Complex Points of Real Surfaces in Complex Sur¬
faces. A4.2. Cancellation of Complex Points. A4.3. Nei¬
ghborhoods of Real Surfaces.
iii
Appendix V. Seiberg Witten Invariants and Envelopes pp. 173 181
A5.1. The Genus Estimate. A5.2. The use of Seiberg
Witten Invariant. A5.3. The Genus Estimate on Stein
Surfaces and Envelopes. A5.4. Two spheres in C2. A5.5.
Attaching Complex Disks to Strictly Pseudonconvex Do¬
mains.
References pp. 182 186 |
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| author | Ivashkovich, Sergei Shevchishin, Vsevolod |
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| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-09-24T00:16:19Z |
| institution | BVB |
| language | English |
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| physical | 186 S. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
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| publisher | Inst. für Mathematik, Ruhr-Univ. |
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| series | Graduiertenkolleg Geometrie und Mathematische Physik <Bochum>: Schriftenreihe des Graduiertenkollegs Geometrie und Mathematische Physik |
| series2 | Graduiertenkolleg Geometrie und Mathematische Physik <Bochum>: Schriftenreihe des Graduiertenkollegs Geometrie und Mathematische Physik |
| spelling | Ivashkovich, Sergei Verfasser aut Complex curves in almost complex manifolds and meromorphic hulls Sergei Ivashkovich ; Vsevolod Shevchishin Bochum Inst. für Mathematik, Ruhr-Univ. 1999 186 S. txt rdacontent n rdamedia nc rdacarrier Graduiertenkolleg Geometrie und Mathematische Physik <Bochum>: Schriftenreihe des Graduiertenkollegs Geometrie und Mathematische Physik 36 Kompaktheit (DE-588)4456100-3 gnd rswk-swf Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd rswk-swf Topologische Hülle (DE-588)4604955-1 gnd rswk-swf Komplexe algebraische Kurve (DE-588)4164890-0 gnd rswk-swf Komplexe algebraische Kurve (DE-588)4164890-0 s Komplexe Mannigfaltigkeit (DE-588)4031996-9 s Kompaktheit (DE-588)4456100-3 s Topologische Hülle (DE-588)4604955-1 s DE-604 Shevchishin, Vsevolod Verfasser aut Graduiertenkolleg Geometrie und Mathematische Physik <Bochum>: Schriftenreihe des Graduiertenkollegs Geometrie und Mathematische Physik 36 (DE-604)BV009298127 36 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009325764&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ivashkovich, Sergei Shevchishin, Vsevolod Complex curves in almost complex manifolds and meromorphic hulls Graduiertenkolleg Geometrie und Mathematische Physik <Bochum>: Schriftenreihe des Graduiertenkollegs Geometrie und Mathematische Physik Kompaktheit (DE-588)4456100-3 gnd Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd Topologische Hülle (DE-588)4604955-1 gnd Komplexe algebraische Kurve (DE-588)4164890-0 gnd |
| subject_GND | (DE-588)4456100-3 (DE-588)4031996-9 (DE-588)4604955-1 (DE-588)4164890-0 |
| title | Complex curves in almost complex manifolds and meromorphic hulls |
| title_auth | Complex curves in almost complex manifolds and meromorphic hulls |
| title_exact_search | Complex curves in almost complex manifolds and meromorphic hulls |
| title_full | Complex curves in almost complex manifolds and meromorphic hulls Sergei Ivashkovich ; Vsevolod Shevchishin |
| title_fullStr | Complex curves in almost complex manifolds and meromorphic hulls Sergei Ivashkovich ; Vsevolod Shevchishin |
| title_full_unstemmed | Complex curves in almost complex manifolds and meromorphic hulls Sergei Ivashkovich ; Vsevolod Shevchishin |
| title_short | Complex curves in almost complex manifolds and meromorphic hulls |
| title_sort | complex curves in almost complex manifolds and meromorphic hulls |
| topic | Kompaktheit (DE-588)4456100-3 gnd Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd Topologische Hülle (DE-588)4604955-1 gnd Komplexe algebraische Kurve (DE-588)4164890-0 gnd |
| topic_facet | Kompaktheit Komplexe Mannigfaltigkeit Topologische Hülle Komplexe algebraische Kurve |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009325764&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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