导语摘要
《卡拉比–丘流形和相关几何》是由2001年夏天norway,nordfjordeid讲述辛几何的讲义扩展而成。突出讲述calabi-yau是本书的*特点。部分讲述完整群和已校准子流形,强调特殊拉格朗日算符子流形和syz猜想;第二部分运用代数几何讲述calabi-yau流形和镜子对称。后一部分讲述紧hyperkahler流形,它具有的几何结果和calabi-yau流形有很大的关系。各部分之间过渡自然,衔接紧密紧密,是一部很好的教程。目次:黎曼完整群和已校准的几何;calabi-yau流形和镜子对称;紧hyperk?hler流形。
读者对象:数学专业的高年级本科生,研究生和科研人员。
目录
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 and
gromov-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
内容摘要
《卡拉比–丘流形和相关几何》是由2001年夏天norway,nordfjordeid讲述辛几何的讲义扩展而成。突出讲述calabi-yau是本书的*特点。部分讲述完整群和已校准子流形,强调特殊拉格朗日算符子流形和syz猜想;第二部分运用代数几何讲述calabi-yau流形和镜子对称。后一部分讲述紧hyperkahler流形,它具有的几何结果和calabi-yau流形有很大的关系。各部分之间过渡自然,衔接紧密紧密,是一部很好的教程。目次:黎曼完整群和已校准的几何;calabi-yau流形和镜子对称;紧hyperk?hler流形。
读者对象:数学专业的高年级本科生,研究生和科研人员。
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