Description
Book SynopsisProvides an introduction to Hodge theory - one of the central and most vibrant areas of contemporary mathematics - from leading specialists on the subject. This book includes topics that range from the basic topology of algebraic varieties to the study of variations of mixed Hodge structure and the Hodge theory of maps.
Trade Review"Charles and Schnell's chapter beautifully surveys the theory of absolute Hodge classes, giving in particular a complete proof of Deligne's theorem on absolute Hodge classes on abelian varieties... A welcome addition to the literature and should be useful to both graduate students and researchers working in Hodge theory."--Dan Petersen, MathSciNet
Table of Contents*FrontMatter, pg. i*Contributors, pg. v*Contents, pg. vii*Preface, pg. xv*Chapter One. Introduction to Kahler Manifolds, pg. 1*Chapter Two. From Sheaf Cohomology to the Algebraic de Rham Theorem, pg. 70*Chapter Three. Mixed Hodge Structures, pg. 123*Chapter Four. Period Domains and Period Mappings, pg. 217*Chapter Five. The Hodge Theory of Maps, pg. 257*Chapter Six The Hodge Theory of Maps, pg. 273*Chapter Seven. Introduction to Variations of Hodge Structure, pg. 297*Chapter Eight. Variations of Mixed Hodge Structure, pg. 333*Chapter Nine. Lectures on Algebraic Cycles and Chow Groups, pg. 410*Chapter Ten. The Spread Philosophy in the Study of Algebraic Cycles, pg. 449*Chapter Eleven. Notes on Absolute Hodge Classes, pg. 469*Chapter Twelve. Shimura Varieties: A Hodge-Theoretic Perspective, pg. 531*Bibliography, pg. 574*Index, pg. 577
