Mathematical Research Letters

Volume 19 (2012)

Number 5

On the coniveau of certain sub-Hodge structures

Pages: 1097 – 1115



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


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.

Published 15 March 2013