Differential Forms on Singular Varieties: De Rham and Hodge Theory Simplified (Chapman & Hall/CRC Pure and Applied Mathematics) 1st Edition by Vincenzo Ancona (PDF)

Description

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 higher dimension than the initial space. It simplifies the theory through easily identifiable and well-defined weight filtrations. It also avoids discussion of cohomological descent theory to maintain accessibility. Topics include classical Hodge theory, differential forms on complex spaces, and mixed Hodge structures on noncompact spaces.

User’s Reviews

Editorial Reviews: Review “… 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

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