THE IRREDUCIBLE COMPONENTS OF THE PRIMAL COHOMOLOGY OF THE THETA DIVISOR OF AN ABELIAN FIVEFOLD

摘要

The primal cohomology K-Q of the theta divisor Theta of a principally polarized abelian fivefold (ppav) is the direct sum of its invariant and anti-invariant parts K-Q(+1), resp. K-Q(-1) under the action of -1. For smooth Theta. these have dimension 6 and 72 respectively. We show that K(Q)(+1 )consists of Hodge classes and, for a very general K-Q(+1) is a simple Hodge structure of level 2.