Differential Forms on Singular Varieties: De Rham and Hodge Theory Simplified

by Vincenzo Ancona, Bernard Gaveau

Overview

Differential Forms on Singular Varieties: De Rham and Hodge Theory Simplified uses complexes of differential forms to give a complete treatment of the Deligne theory of mixed Hodge structures on the cohomology of singular spaces. This book features an approach that employs recursive arguments on dimension and does not introduce spaces of hig

Product Details

ISBN-13:	9781040204023
Publisher:	CRC Press
Publication date:	08/24/2005
Series:	Chapman & Hall/CRC Pure and Applied Mathematics
Sold by:	Barnes & Noble
Format:	eBook
Pages:	312
File size:	1 MB

About the Author

Vincenzo Ancona, Bernard Gaveau

Table of Contents

Classical Hodge Theory. Spectral Sequences and Mixed Hodge Structures. Complex Manifolds, Vector Bundles, Differential Forms. Sheaves and Cohomology. Harmonic Forms on Hermitian Manifolds. Hodge Theory on Compact K erian Manifolds. The Theory of Residues on a Smooth Divisor. Complex Spaces. Differential Forms on Complex Spaces. The Basic Example. Differential Forms in Complex Spaces. Mixed Hodge Structures on Compact Spaces. Mixed Hodge Structures on Noncompact Spaces. Residues and Hodge Mixed Structures: Leray Theory. Residues and Mixed Hodge Structures on Noncompact Manifolds. Mixed Hodge Structures in Noncompact Spaces: The Basic Example. Mixed Hodge Structures on Noncompact Singular Spaces.

Editorial Reviews

… is divides into three parts of roughly 100 pages each. … written for people who have  a basic understanding of the subject and who wish to see what’s happening behind the scenes. … material more accessible. ”
— Donu Arapura, Purdue University, in Siam Review, Vol. 48, No. 3
“This book offers a novel and complete treatment of the Deligne theory of mixed Hodge structures on the cohomology of singular spaces. … well-written for an advanced level text ant it is valuable to beginning researchers as an introduction to an important and beautiful mathematical subject. The book will also serve as a good reference for further research work.”
— Vagn Lundsgaard Hansen (Lyngby), in Zentralblatt MATH 1088

From the Publisher