Weight filtration on the cohomology of complex analytic spaces

Joana Cirici and Francisco Guillén

Journal of Singularities
volume 8 (2014), 83-99

Received: 8 April 2014. Received in revised form: 2 September 2014.

DOI: 10.5427/jsing.2014.8g

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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 compactifiable 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:

weight filtration, cohomological descent, cubical hyperresolutions, mixed Hodge theory, analytic spaces

Mathematical Subject Classification:

32C18 (primary), 32S35 (secondary)

Author(s) information:

Joana Cirici	Francisco Guillén
Fachbereich Mathematik und Informatik	Departament d'Àlgebra i Geometria
Freie Universität Berlin, Arnimallee 3	Universitat de Barcelona, Gran Via 585
14195 Berlin, Germany	08007 Barcelona, Spain
email: jcirici@math.fu-berlin.de	email: fguillen@ub.edu