The Fano surface of the Fermat cubic threefold, the del Pezzo surface of degree 5 and a ball quotient

Details The Fano surface of the Fermat cubic threefold, the del Pezzo surface of degree 5 and a ball quotient The Fano surface of the Fermat cubic threefold, the del Pezzo surface of degree 5 and a ball quotient

2010-01-28

arxiv.org/abs/1001.5111v2

Mathematics

Algebraic Geometry

8 pages, extended and final version, to appear in the Proc. of. A.M.S

Scientific paper

We study the Fano surface S of the Fermat cubic threefold. We prove that S is
a degree 81 abelian cover of the degree 5 del Pezzo surface and that the
complement of the union of 12 disjoint elliptic curves on S is a ball quotient.
The lattice of this ball quotient is related to the Deligne-Mostow lattice
number 1.

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