On the coniveau of certain sub-Hodge structures

Abstract

We study the generalized Hodge conjecture for certain sub-Hodge structure defined as the kernel of the cup product map with a big cohomology class, which is of Hodge coniveau at least 1. As predicted by the generalized Hodge conjecture, we prove that the kernel is supported on a divisor, assuming the Lefschetz standard conjecture.

arXiv comment23 pages. V2: Typos corrected. Comments still welcome. To appear in Math.Res.Lett

References in corpus (1)

• The generalized Hodge and Bloch conjectures are equivalent for general complete intersections