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Gross M., Huybrechts D., Joyce D. — Calabi-Yau Manifolds and Related Geometries: Lectures at a Summer School in Nordfjordeid, Norway, June 2001
Gross M., Huybrechts D., Joyce D. — Calabi-Yau Manifolds and Related Geometries: Lectures at a Summer School in Nordfjordeid, Norway, June 2001

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Название: Calabi-Yau Manifolds and Related Geometries: Lectures at a Summer School in Nordfjordeid, Norway, June 2001

Авторы: Gross M., Huybrechts D., Joyce D.

Аннотация:

This book is an expanded version of lectures given at a summer school on symplectic geometry in Nordfjordeid, Norway, in June 2001. The unifying feature of the book is an emphasis on Calabi-Yau manifolds. The first part discusses holonomy groups and calibrated submanifolds, focusing on special Lagrangian submanifolds and the SYZ conjecture. The second studies Calabi-Yau manifolds and mirror symmetry, using algebraic geometry. The final part describes compact hyperkahler manifolds, which have a geometric structure very closely related to Calabi-Yau manifolds.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 228

Добавлена в каталог: 20.11.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$G_2$      15 27—28
$G_2-$manifold      28
$G_2-$structure      27
$\hat A—$genus      29
Almost Calabi — Yau m-folds      54
Associateive 3-folds      36 40 56
Associateive 3-folds deformations      41 56
Asymptotic cone      44 59
Atiyah — Singer index theorem      56
Beauville — Bogomolov form      173
Beauville — Bogomolov form of the generalized Kummer      179
Beauville — Bogomolov form of the Hilbert scheme      178
Beauville — Bogomolov form unnormalized      203
Berger's theorem      13—14
Bianchi identities      10 11
Calabi Conjecture      21—24
Calabi — Yau m-folds      15 18—19
Calabi — Yau m-folds almost      54
Calabi — Yau m-folds constructions      25 26
Calibrated geometry      32—36
Calibrated submanifolds      33
Calibrated submanifolds compact      50
Calibration      18 33
Calibration maximal      35
Canonical bundle      18
Cayley 4-folds      36 41 56
Cayley 4-folds deformations      41 56
Chern class      19
Coassociative 4-folds      36 40 55
Coassociative 4-folds deformations      41 56
Complete intersection      25
Complex manifold      16
Complex structure      16
Complex symplectic structure      20
Connection      7
Crepant resolution      26
Current, positive      197
Curvature      8
Curvature constant      13
Deformation      163
Deformation universal      164
Deformation unobstructed      165 194
Dolbeault cohomology      24
Exceptional holonomy groups      15 27—32
Exceptional holonomy groups compact manifolds      29—31
Fibration      161 185
FORM      7
Form holomorphic volume      18
Form Kaehler      17
Form Ricci      18
Geometric measure theory      32 33 36 58
Hilbert scheme      157 160
Hodge number      24
Holomorphyic volume form      18
Holonomy group and constant tensors      9
Holonomy group and curvature      9
Holonomy group of a connection      9
Holonomy group of a metric      11
Holonomy group properties      9
HRR-formula      178
Hyperkaehler geometry      15 20
Jacobi identity      11
K3 surface      24 155
K3 surface elliptic      156 162 186
K3 surface Fermat quartic      156
K3 surface Kummer surface      156
Kaehler class      17
Kaehler cone      169 197 211
Kaehler cone birational      214
Kaehler cone of a very general      191 198
Kaehler form      17
Kaehler geometry      15—17
Kaehler potential      17
Kodaira — Spencer class      163
Kodaira — Spencer class of the twistor space      189
Kummer variety, generalized      158 179 193 199
Lagrangian submanifolds      38
Legendrian index      60
Levi-Civita connection      10
Lie bracket      7
Manifold hyperkaehler      169
Manifold, irreducible holomorphic symplectic      155
Manifold, irreducible holomorphic symplectic birational      158 161 166 192 203 208
Marked manifold      188
Metric      10
Metric Calabi — Yau      15
Metric Hermitian      17
Metric hyperkaehler      15 20
Metric irreducible      12
Metric Kaehler      15
Metric locally symmetric      13
Metric nonsymmetric      13
Metric product      12
Metric quaternionic Kaehler      15
Metric reducible      12
Minimal submanifolds      32—33
Mirror Symmetry      64—65
Moduli space      188
Moment map      42 45 49
Mukai      159 166 204
Nijenhuis tensor      16
Octonions      15
Parallel transport      9
Period domain      167 188 190
Period map      168 188
Period map surjectivity      190
Quaternions      15 20 38
Quintic      26
Resolution      26
Resolution crepant      26
Ricci curvature      18
Ricci form      18
Riemann curvature      10
Riemannian metric      see metric
Special Lagrangian cones      42 58—61
Special Lagrangian cones rigid      61
Special Lagrangian cones, as an integrable system      44
Special Lagrangian cones, examples      47 48
Special Lagrangian fibrations      65—69
Special Lagrangian fibrations, discriminant      65 67
Special Lagrangian fibrations, singularities      66—69
Special Lagrangian m-folds      36—40
Special Lagrangian m-folds compact      51—55
Special Lagrangian m-folds in almost Calabi — Yau m-folds      54
Special Lagrangian m-folds ruled      44
Special Lagrangian m-folds strongly AC      58
Special Lagrangian m-folds weakly AC      58
Special Lagrangian m-folds with phase $\e^{i\theta}$      37
Special Lagrangian m-folds, affine structures on moduli space      53—54
Special Lagrangian m-folds, Asymptotically Conical      58
Special Lagrangian m-folds, constructions      42—49
Special Lagrangian m-folds, deformations      39—40 50—52 59—60
Special Lagrangian m-folds, examples      47—49
Special Lagrangian m-folds, index of singularities      62 68
Special Lagrangian m-folds, obstructions      50 52—53
Special Lagrangian m-folds, singularities      50 57—63
Special Lagrangianbration      50
Spin(7)      15 28—29
Spin(7)-manifold      29
Spin(7)-structure      28
String theory      64
Symmetric space      12
SYZ Conjecture      63—69
Tangent cone      36 58
Tensors      6
Tensors, constant      9 11
Tensors, Einstein summation convention      7
Tensors, index notation      7
Torelli theorem global      192
Torelli theorem global for K3 surfaces      192
Torelli theorem global, counterexample      193
Torelli theorem local      168
Toric variety      26
Torsion      8
Twistor space      187
Vector bundles      6
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