Geodesic
Weight filtration on the cohomology of complex analytic spaces
Journal of Singularities, Tome 8 (2014), pp. 83-99

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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.
DOI : 10.5427/jsing.2014.8g
Classification : 32C18(primary), 32S35(secondary) 
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     author = {Joana Cirici and Francisco Guill\'en},
     title = {Weight filtration on the cohomology of complex analytic spaces},
     journal = {Journal of Singularities},
     pages = {83--99},
     publisher = {mathdoc},
     volume = {8},
     year = {2014},
     doi = {10.5427/jsing.2014.8g},
     url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2014.8g/}
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Joana Cirici; Francisco Guillén. Weight filtration on the cohomology of complex analytic spaces. Journal of Singularities, Tome 8 (2014), pp. 83-99. doi: 10.5427/jsing.2014.8g

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