《卡拉比–丘流形和相關幾何》是由2001年夏天norway，nordfjordeid講述辛幾何的講義擴展而成。突出講述calabi-yau是本書的最大特點。第一部分講述完整群和已校準子流形，強調特殊拉格朗日算符子流形和syz猜想；第二部分運用代數(shù)幾何講述calabi-yau流形和鏡子對稱。最后一部分講述緊hyperkahler流形，它具有的幾何結果和calabi-yau流形有很大的關系。各部分之間過渡自然，銜接緊密緊密，是一部很好的教程。目次：黎曼完整群和已校準的幾何；calabi-yau流形和鏡子對稱；緊hyperk?hler流形。
讀者對象：數(shù)學專業(yè)的高年級本科生，研究生和科研人員。
preface
part i. riemannian holonomy groups and calibrated geometry
dominic joyce
1 introduction
2 introduction to holonomy groups
3 berger's classification of holonomy groups
4 kahler geometry and holonomy
5 the calabi conjecture
6 the exceptional holonomy groups
7 introduction to calibrated geometry
8 calibrated submanifolds in rn
9 constructions of sl m-folds in ctm
10 compact calibrated submanifolds
11 singularities of special lagrangian m-folds
12 the syz conjecture, and sl fibrations
preface
part i. riemannian holonomy groups and calibrated geometry
dominic joyce
1 introduction
2 introduction to holonomy groups
3 berger's classification of holonomy groups
4 kahler geometry and holonomy
5 the calabi conjecture
6 the exceptional holonomy groups
7 introduction to calibrated geometry
8 calibrated submanifolds in rn
9 constructions of sl m-folds in ctm
10 compact calibrated submanifolds
11 singularities of special lagrangian m-folds
12 the syz conjecture, and sl fibrations
part ii. calabi-yau manifolds and mirror symmetry
mark gross
13 introduction
14 the classical geometry of calabi-yau manifolds
15 kahler moduli andgromov-witten invariants
16 variation and degeneration of hodge structures
17 a mirror conjecture
18 mirror symmetry in practice
19 the strominger-yau-zaslow approach to mirror symmetry
part iii. compact hyperkaihler manifolds
daniel huybrechts
20 introduction
21 holomorphic symplectlc manifolds
22 deformations of complex structures
23 the beauville-bogomolov form
24 cohomology of compact hyperkahler manifolds
25 twistor space and moduli space
26 projectivity of hyperkahler manifolds
27 birational hyperkahler manifolds
28 the (birational) kahler cone
references
index
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