Weight filtration on the cohomology of complex analytic spaces
Algebraic Geometry
2014-09-30 v2
Abstract
We extend Deligne's weight filtration to the integer cohomology of complex analytic spaces (endowed with an equivalence class of compactifications). In general, the weight filtration that we obtain is not part of a mixed Hodge structure. Our purely geometric proof is based on cubical descent for resolution of singularities and Poincar\'e-Verdier duality. Using similar techniques, we introduce the singularity filtration on the cohomology of compactificable analytic spaces. This is a new and natural analytic invariant which does not depend on the equivalence class of compactifications and is related to the weight filtration.
Keywords
Cite
@article{arxiv.1403.6805,
title = {Weight filtration on the cohomology of complex analytic spaces},
author = {Joana Cirici and Francisco Guillén},
journal= {arXiv preprint arXiv:1403.6805},
year = {2014}
}
Comments
examples added + minor corrections