Differential forms on singular varieties De Rham and Hodge theory simplified 1st Edition by Vincenzo Ancona 9781420026528 1420026526
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ISBN 10: 1420026526
ISBN 13: 9781420026528
Author: Vincenzo Ancona
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
Differential forms on singular varieties De Rham and Hodge theory simplified 1st Table of contents:
Part I: Classical Hodge theory
Chapter 1: Spectral sequences and mixed Hodge structures
Chapter 2: Complex manifolds, vector bundles, differential forms
Chapter 3: Sheaves and cohomology
Chapter 4: Harmonic forms on hermitian manifolds
Chapter 5: Hodge theory on compact kählerian manifolds
Chapter 6: The theory of residues on a smooth divisor
Chapter 7: Complex spaces
Part II: Differential forms on complex spaces
Chapter 1: The basic example
Chapter 2: Differential forms on complex spaces
Chapter 3: Mixed Hodge structures on compact spaces
Part III: Mixed Hodge structures on noncompact spaces
Chapter 1: Residues and Hodge mixed structures: Leray theory
Chapter 2: Residues and mixed Hodge structures on noncompact manifolds
Chapter 3: Mixed Hodge structures on noncompact spaces: the basic example
Chapter 4: Mixed Hodge structures on noncompact singular spaces
References
Index
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Vincenzo Ancona,Differential,singular