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

2010/01/28 by Xavier Roulleau, Roulleau, Xavier
Mathematics · #14J25 #14J29 #22E40 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1001.5111

openalex publication_date 2010/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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