ABSTRACT

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

part |2 pages

I Classical Hodge theory

chapter 3|22 pages

Sheaves and cohomology

chapter 4|22 pages

Harmonic forms on hermitian manifolds

chapter 7|24 pages

Complex spaces

part |2 pages

II Differential forms on complex spaces

chapter 1|14 pages

The basic example

chapter 2|32 pages

Differential forms on complex spaces

chapter 3|26 pages

Mixed Hodge structures on compact spaces

part |2 pages

III Mixed Hodge structures on noncompact spaces