Steven Zucker教授在代数几何中的Hodge理论、L^2和L^p (p ≠ 2)上同调以及局部对称空间的紧化等领域做出了重要的贡献,并于20世纪80年代提出了著名的Zucker猜想。本书的内容涉及了Zucker教授研究和关注的相关领域,由Ayoub, Bierstone, Griffiths, M. Green, Hain, Ohsawa等该领域的知名专家精心写成,包含了关于Hodge理论、复分析和几何中的L2方法以及代数几何中的相关结果的研究和介绍性文章。
Preface
The Research Career of Steven Zucker: An Autobiographical Account
On the Hodge Theory of Stratified Spaces
Simpson's Construction of Varieties with Many Local Systems
Motives and Algebraic Cycles: A Selection of Conjectures and Open Questions
Resolution of Singularities of Differential Forms and Hsiang-Pati Coordinates
Nilpotent Cones and Their Representation Theory
Recent Results on Cohomology Jump Loci
On Semipositivity,Injectivity and Vanishing Theorems
The Business of Height Pairings
Extremal Degenerations of Polarized Hodge Structures
Deligne-Beilinson Cohomology of Affine Groups
Singularities in Arbitrary Characteristic via Jet Schemes
Extended Period Domains, Algebraic Groups, and Higher Albanese Manifolds
Motivic and Automorphic Aspects of the Reductive Borel-Serre Compactification
An Update of Extension Theorems by the L2 Estimates for ?
A Young Person's Guide to Mixed Hodge Modules
Perverse Sheaves and the Reductive Borel-Serre Compactification
Nonlinear Harmonic Forms and Indefinite Bochner Formulas