Mixed Hodge Structures

• Main Authors: Peters, Chris A.M (Author), Steenbrink, Joseph H.M (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2008.
• Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics ; 52
• Subjects: Mathematics.; Algebra.; Algebraic geometry.; Differential geometry.; Topology.; Physics.; Algebraic Geometry.; Differential Geometry.; Mathematical Methods in Physics.

The text of this book has its origins more than twenty- ve years ago. In the seminar of the Dutch Singularity Theory project in 1982 and 1983, the second-named author gave a series of lectures on Mixed Hodge Structures and Singularities, accompanied by a set of hand-written notes. The publication of...

Table of Contents:

• Basic Hodge Theory
• Compact Kähler Manifolds
• Pure Hodge Structures
• Abstract Aspects of Mixed Hodge Structures
• Mixed Hodge Structures on Cohomology Groups
• Smooth Varieties
• Singular Varieties
• Singular Varieties: Complementary Results
• Applications to Algebraic Cycles and to Singularities
• Mixed Hodge Structures on Homotopy Groups
• Hodge Theory and Iterated Integrals
• Hodge Theory and Minimal Models
• Hodge Structures and Local Systems
• Variations of Hodge Structure
• Degenerations of Hodge Structures
• Applications of Asymptotic Hodge Theory
• Perverse Sheaves and D-Modules
• Mixed Hodge Modules.