几何与分析（第II卷）

出版时间：2010-9  出版社：高等教育出版社  作者：季理真 编  页数：563  

内容概要

　　The launch of this Advanced Lectures in Mathematics series is aimed at keeping mathematicians informed of the latest developments in mathematics， as well as toaid in the learning of new mathematical topics by students all over the world. Each volume consists of either an expository monograph or a collection of signify cant introductions to important topics， This series emphasizes the history and sources of motivation for the topics under discussion， and also gives an overview of the current status of research in each particular field. These volumes are the first source to which people will turn in order to learn new subjects and to dis cover the latest results of many cutting-edge fields in mathematics. 　　This book contains many substantial papers from distinguished speakers of a conference ”Geometric Analysis： Present and Future" and an overview of the works of Professor Shing-Tung Yau. Contributors include E. Witten， Y.T. Siu， R. Hamilton， H. Hitchin， B. Lawson， A. Strominger， C. Vafa， W. Schmid， V. Guillemin， N. Mok， D. Christodoulou. This is a valuable reference that gives an up-to-dated summary of geometric analysis and its applications in many different areas of mathematics.

书籍目录

Part 3 Mathematical Physics， Algebraic Geometry and Other TopicsThe Coherent-Constructible Correspondence and Homological Mirror Symmetry for Toric VarietiesBohan Fang， Chiu-Chu Melissa Liu， David Treumann and Eric Zaslow.1 Introduction1.1 Outline2 Mirror symmetry for toric manifolds2.1 Hori-Vafa mirror2.2 Categories in mirror symmetry2.3 Results to date3 T-duality3.1 Moment polytope3.2 Geometry of the open orbit3.3 Statement of symplectic results3.4 T-dual of an equivariant line bundle4 Microlocalization4.1 Algebraic preliminaries4.2 The cast of categories4.3 Fukaya-Oh theorem4.4 Building the equivalence4.5 Equivalence and the inverse functor4.6 Singular support and characteristic cycles4.7 Comments on technicalities4.8 Statement of results5 Coherent-constructible correspondence6 Examples6.1 Taking the mapping cone6.2 Toric Fano surfaces6.3 Hirzebruch surfacesReferencesSuperspace： a Comfortably Vast Algebraic VarietyT. Hiibsch1 Introduction1.1 Basic ideas and definitions1.2 The traditional superspace2 Off-shell worldline supermultiplets2.1 Adinkraic supermultiplets2.2 Various hangings2.3 Projected supermultiplets2.4 Supermultiplets vs. superfields3 Superspace， by construction3.1 Superpartners of time3.2 A telescoping deformation structure3.3 Nontrivial superspace geometry3.4 Higher-dimensional spacetime4 The comfortably vast superspaceReferencesA Report on the Yau-Zaslow FormulaNaichung Conan Leung1 Yau-Zaslow formula and its generalizations2 Yau-Zaslow approach3 Matching method4 Degeneration method5 Calabi-Yau threefold method6 ConclusionsReferencesHermitian-Yang-Mills Connections on Kahler ManifoldsJun Li1 Introduction1.1 Hermitian-Yang-Mills connections1.2 HYM connections lead to stable bundles1.3 Stable bundles and their moduli spaces1.4 Flat bundles and stable bundles on curves2 Donaldson-Uhlenbeck-Yau theorem2.1 Donaldsons proof for algebraic surfaces2.2 Uhlenbeck-Yaus proof for Kahler manifolds3 Hermitian-Yang-Mills connections on curves4 Hermitian-Yang-Mills connections on surfaces4.1 Extending DUY correspondence4.2 Stable topology of the moduli spaces4.3 Donaldson polynomial invariants5 HYM connections on high dimensional varieties5.1 Extending the DUY correspondence in high dimensions5.2 Donaldson-Thomas invariants6 Concluding remarkReferences ~Additivity and Relative Kodaira DimensionsTian-Jun Li and Weiyi Zhang1 Introduction2 Kodaira Dimensions and fiber bundles2.1 h for complex manifolds and up to dimension 32.2 Ks for symplectic 4~manifolds 2.3 Additivity for a fiber bundle3 Embedded symplectic surfaces and relative Kod. dim. in dim. 4.3.1 Embedded symplectic surfaces and maxinmlity3.2 The adjoint class3.3 Existence and Uniqueness of relatively minimal model3.4 （M，w，F)4 Relative Kod. dim. in dim. 2 and fibrations over a surface4.1 （F，D)， Riemann-Hurwitz formula and Seifert fibrations...4.2 Lefschetz fibrationsReferencesDescendent Integrals and Tautological Rings ofModuli Spaces of CurvesKefen9 Liu and Hao Xu1 Introduction2 Intersection numbers and the Witten-Kontsevich theorem2.1 Witten-Kontsevich theorem2.2 Virasoro constraints3 The n-point function3.1 A recursive formula of n-point functions3.2 An effective recursion formulae of descendent integrals4 Hodge integrals4.1 Fabers algorithm4.2 Hodge integral formulae5 Higher Weil-Petersson volumes5.1 Generalization of Mirzakhanis recursion formula5.2 Recursion formulae of higher Weil-Petersson volumes6 Fabers conjecture on tautological rings6.1 The Faber intersection number conjecture6.2 Relations with n-point functions7 Dimension of tautological rings7.1 Ramanujans mock theta functions7.2 Asymptotics of tautological dimensions8 Gromov-Witten invariants8.1 Universal equations of Gromov-Witten invariants8.2 Some vanishing identities9 Wittens r-spin numbers9.1 Generalized Wittens conjecture9.2 An algorithm for computing Wittens r-spin numbersReferencesA General Voronoi Summation Formula for GL（n， Z)Stephen D. Miller and Wilfried Sehmid1 Introduction2 Automorphic Distributions3 Vanishing to infinite order4 Classical proof of the formula 5 Adelic proof of the formulaReferencesGeometry of Holomorphic Isometries and Related Mapsbetween Bounded DomainsNgaiming Mok1 Examples of holomorphic isometries1.1 Examples of equivariant embeddings into theprojective space1.2 Non-standard holomorphic isometries of the Poincardisk into polydisks1.3 A non-standard holomorphic isometry of the Poincardisk into a Siegel upper half-plane1.4 Examples of holomorphic isometries with arbitrarynormalizing constants A > 12 Analytic continuation of germs of holomorphic isometries2.1 Analytic continuation of holomorphic isometries into theprojective space equipped with the Fubini-Study metric2.2 An extension and rigidity problem arising fromcommutators of modular correspondences2.3 Analytic continuation of holomorphic isometries up tonormalizing constants with respect to the Bergmanmetric - extension beyond the boundary2.4 Canonically embeddable Bergman manifolds andBergman meromorphic compactifications3 Holomorphic isometries of the Poincar disk intobounded symmetric domains3.1 Structural equations on the norm of the secondfundamental form and asymptotic vanishing order3.2 Holomorphic isometries of the Poincar disk intopolydisks： structural results3.3 Calculated examples on the norm of the secondfundamental form3.4 Holomorphic isometries of the Poincar5 disk intopolydisks： uniqueness results3.5 Asymptotic total geodesy and applications4 Measure-preserving algebraic correspondences on irreduciblebounded symmetric domains4.1 Statements of results4.2 Extension results on strictly pseudoconvexalgebraic hypersurfaces4.3 Alexander-type extension results in the higher-rank case 4.4 Total geodesy of germs of measure-preserving holomorphie