章节目录
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
内容简介
《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是本书的最大特点。第一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。最后一部分讲述紧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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