The transcendental lattice of the sextic Fermat surface

Abstract

We prove that the integral polarized Hodge structure on the transcendental lattice of a sextic Fermat surface is decomposable. This disproves a conjecture of Kulikov related to a Hodge theoretic approach to proving the irrationality of the very general cubic fourfold.

15 pages; v2: minor changes, streamlined the argument in Section 4