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Published version

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2014-09-02

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/62384

Weight filtration on the cohomology of complex analytic spaces

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http://dx.doi.org/10.5427/jsing.2014.8g

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.

Subject

Espais analítics, Singularitats (Matemàtica)

Subject (English)

Analytic spaces, Singularities (Mathematics)

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Articles publicats en revistes (Matemàtiques i Informàtica)

Citation

CIRICI, Joana and GUILLÉN SANTOS, Francisco. Weight filtration on the cohomology of complex analytic spaces. Journal of Singularities. 2014. Vol. 8, num. 83-99. ISSN 1949-2006. [consulted: 8 of August of 2026]. Available at: https://hdl.handle.net/2445/62384

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