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Weight filtration on the cohomology of complex analytic spaces

By Joana Cirici and Francisco Guillén Santos

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 Poincaré-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

Topics: Espais analítics, Singularitats (Matemàtica), Analytic spaces, Singularities (Mathematics)
Publisher: Worldwide Center of Mathematics
Year: 2015
DOI identifier: 10.5427/jsing.2014.8g
OAI identifier: oai:diposit.ub.edu:2445/62384
Journal:

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