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

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.

preprint2010arXivOpen access
Xavier Roulleau
math.AG
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Xavier Roulleau

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