Mathematical Research Letters

Volume 20 (2013)

Number 6

The transcendental lattice of the sextic Fermat surface

Pages: 1017 – 1031



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)


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.


Fermat surface, cubic fourfold, rationality, transcendental lattice

2010 Mathematics Subject Classification

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

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