Two coniveau filtrations

Abstract

A cohomology class of a smooth complex variety of dimension $n$ has coniveau $\ge c$ if it vanishes in the complement of a closed subvariety of codimension $\ge c$, and has strong coniveau $\ge c$ if it comes by proper pushforward from the cohomology of a smooth variety of dimension $\le n-c$. We show that these two notions differ in general, both for integral classes on smooth projective varieties and for rational classes on smooth open varieties.

26 pages, final version

Cited by in corpus (2)

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