Mirror symmetry and algebraic geometry:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhodes Island
American Mathematical Society
[1999]
|
| Series: | Mathematical surveys and monographs
Volume 68 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xxi, 469 Seiten |
| ISBN: | 0821810596 9780821821275 |
Staff View
MARC
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| 245 | 1 | 0 | |a Mirror symmetry and algebraic geometry |c David A. Cox ; Sheldon Katz |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface xiii
Goal of the Book xiii
Relation to Physics xiv
How to Read the Book xv
Acknowledgements xvii
Our Hope xviii
Notation xix
Chapter 1. Introduction 1
1.1. The Physics of Mirror Symmetry 1
1.2. Three Point Functions 6
1.3. Why Calabi Yau Manifolds? 10
1.4. The Mathematics of Mirror Symmetry 10
1.5. What s Next? 12
Chapter 2. The Quintic Threefold 15
2.1. The A Model Correlation Function of the Quintic Threefold 15
2.2. The Quintic Mirror 17
2.3. The Mirror Map 19
2.4. The B Model Correlation Function 21
2.5. Putting It All Together 22
2.6. The Mirror Theorems 24
Chapter 3. Toric Geometry 31
3.1. Cones and Fans 31
3.2. Polytopes and Homogeneous Coordinates 33
3.3. Kahler Cones and Symplectic Geometry 38
3.4. The GKZ Decomposition 42
3.5. Fano Varieties and Reflexive Polytopes 46
3.6. Automorphisms of Toric Varieties 47
3.7. Examples 49
Chapter 4. Mirror Symmetry Constructions 53
4.1. The Batyrev Mirror Construction 53
4.2. The Quintic Threefold, Revisited 61
4.3. Toric Complete Intersections 62
4.4. The Voisin Borcea Construction 65
Chapter 5. Hodge Theory and Yukawa Couplings 73
5.1. Hodge Theory 73
ix
x CONTENTS
5.2. Maximally Unipotent Monodromy 78
5.3. The Griffiths Dwork Method 83
5.4. Examples 87
5.5. Hypergeometric Equations 90
5.6. Yukawa Couplings 102
Chapter 6. Moduli Spaces 113
6.1. Complex Moduli 113
6.2. Kahler Moduli 127
6.3. The Mirror Map 148
Chapter 7. Gromov Witten Invariants 167
7.1. Definition via Algebraic Geometry 168
7.2. Definition via Symplectic Geometry 184
7.3. Properties of Gromov Witten Classes 191
7.4. Computing Gromov Witten Invariants, I 196
Chapter 8. Quantum Cohomology 217
8.1. Small Quantum Cohomology 217
8.2. Big Quantum Cohomology 229
8.3. Computing Gromov Witten Invariants, II 234
8.4. Dubrovin Formalism 239
8.5. The A Variation of Hodge Structure 242
8.6. The Mirror Conjecture 257
Chapter 9. Localization 275
9.1. The Localization Theorem 275
9.2. Localization in M0,n(Pr,d) 282
9.3. Equivariant Gromov Witten Invariants 298
Chapter 10. Quantum Differential Equations 301
10.1. Gravitational Correlators 301
10.2. The Givental Connection 311
10.3. Relations in Quantum Cohomology 320
Chapter 11. The Mirror Theorem 331
11.1. The Mirror Theorem for the Quintic Threefold 332
11.2. Givental s Approach 356
Chapter 12. Conclusion 397
12.1. Reflections and Open Problems 397
12.2. Other Aspects of Mirror Symmetry 400
Appendix A. Singular Varieties 407
A.I. Canonical and Terminal Singularities 407
A.2. Orbifolds 408
A.3. Differential Forms on Orbifolds 409
A.4. The Tangent Sheaf of an Orbifold 410
A.5. Symplectic Orbifolds 410
Appendix B. Physical Theories 411
B.I. General Field Theories 411
CONTENTS xi
B.2. Nonlinear Sigma Models 419
B.3. Conformal Field Theories 423
B.4. Landau Ginzburg Models 426
B.5. Gauged Linear Sigma Models 428
B.6. Topological Quantum Field Theories 430
Bibliography 437
Index 453
|
| any_adam_object | 1 |
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| dewey-full | 516.3/62 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/62 |
| dewey-search | 516.3/62 |
| dewey-sort | 3516.3 262 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV012574162 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:29:56Z |
| institution | BVB |
| isbn | 0821810596 9780821821275 |
| language | English |
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| physical | xxi, 469 Seiten |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spelling | Cox, David A. 1948- Verfasser (DE-588)137410832 aut Mirror symmetry and algebraic geometry David A. Cox ; Sheldon Katz Providence, Rhodes Island American Mathematical Society [1999] © 1999 xxi, 469 Seiten txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs Volume 68 Algebraische Geometrie - Mathematische Physik - Spiegelsymmetrie Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Spiegelsymmetrie (DE-588)4538605-5 gnd rswk-swf Spiegelsymmetrie (DE-588)4538605-5 s Algebraische Geometrie (DE-588)4001161-6 s DE-604 Katz, Sheldon 1956- Verfasser (DE-588)137653484 aut Erscheint auch als Online-Ausgabe 978-1-4704-1295-1 Mathematical surveys and monographs Volume 68 (DE-604)BV000018014 68 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008539548&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cox, David A. 1948- Katz, Sheldon 1956- Mirror symmetry and algebraic geometry Mathematical surveys and monographs Algebraische Geometrie - Mathematische Physik - Spiegelsymmetrie Algebraische Geometrie (DE-588)4001161-6 gnd Spiegelsymmetrie (DE-588)4538605-5 gnd |
| subject_GND | (DE-588)4001161-6 (DE-588)4538605-5 |
| title | Mirror symmetry and algebraic geometry |
| title_auth | Mirror symmetry and algebraic geometry |
| title_exact_search | Mirror symmetry and algebraic geometry |
| title_full | Mirror symmetry and algebraic geometry David A. Cox ; Sheldon Katz |
| title_fullStr | Mirror symmetry and algebraic geometry David A. Cox ; Sheldon Katz |
| title_full_unstemmed | Mirror symmetry and algebraic geometry David A. Cox ; Sheldon Katz |
| title_short | Mirror symmetry and algebraic geometry |
| title_sort | mirror symmetry and algebraic geometry |
| topic | Algebraische Geometrie - Mathematische Physik - Spiegelsymmetrie Algebraische Geometrie (DE-588)4001161-6 gnd Spiegelsymmetrie (DE-588)4538605-5 gnd |
| topic_facet | Algebraische Geometrie - Mathematische Physik - Spiegelsymmetrie Algebraische Geometrie Spiegelsymmetrie |
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