Mathematical Research Letters

Volume 19 (2012)

Number 5

On the coniveau of certain sub-Hodge structures

Pages: 1097 – 1115

DOI: http://dx.doi.org/10.4310/MRL.2012.v19.n5.a11

Author

Lie Fu (Département de Mathématiques et Applications, ´Ecole Normale Supérieure, Paris, France)

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.

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