Mathematical Research Letters

Volume 20 (2013)

Number 6

The transcendental lattice of the sextic Fermat surface

Pages: 1017 – 1031

DOI: https://dx.doi.org/10.4310/MRL.2013.v20.n6.a2

Authors

Asher Auel (Department of Mathematics, Yale University, New Haven, Connecticut, U.S.A.)

Christian Böhning (Fachbereich Mathematik, Universität Hamburg, Germany)

Hans-Christian Graf von Bothmer (Fachbereich Mathematik, Universität Hamburg, Germany)

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.

Keywords

Fermat surface, cubic fourfold, rationality, transcendental lattice

2010 Mathematics Subject Classification

14C30, 14D06, 14E08, 14J25, 14Q10

Full Text (PDF format)

Accepted 5 November 2013

Published 13 June 2014