Calabi-Yau流形和相关几何（英文影印版） 出版时间：2011年版 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。 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 manifolds15 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
