Two coniveau filtrations

Olivier Benoist (1, 2) , John Christian Ottem

1 CNRS - Centre National de la Recherche Scientifique
2 DMA - Département de Mathématiques et Applications - ENS Paris

A cohomology class of a smooth complex variety of dimension n has coniveau at least c if it vanishes in the complement of a closed subvariety of codimension at least c, and has strong coniveau at least c if it comes by proper pushforward from the cohomology of a smooth variety of dimension at most 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.

Domaines: Géométrie algébrique [math.AG]

Olivier Benoist, John Christian Ottem. Two coniveau filtrations. Duke Mathematical Journal, 2021, 170, pp.2719-2753. ⟨10.1215/00127094-2021-0055⟩. ⟨hal-03366797⟩