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

1st Edition

Vincenzo Ancona, Bernard Gaveau

Chapman and Hall/CRC
Published August 24, 2005
Reference - 312 Pages
ISBN 9780849337390 - CAT# DK6027
Series: Chapman & Hall/CRC Pure and Applied Mathematics

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Summary

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.

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