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

Roulleau, Xavier

doi:10.1090/S0002-9939-2011-10847-5

The Fano surface of the Fermat cubic threefold, the del Pezzo surface of degree $5$ and a ball quotient
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Proc. Amer. Math. Soc. 139 (2011), 3405-3412 Request permission

Abstract:

In this paper we study a surface which has many intriguing and puzzling aspects: on one hand it is related to the Fano surface of lines of a cubic threefold, and on the other hand it is related to a ball quotient occurring in the realm of hypergeometric functions, as studied by Deligne and Mostow. It is moreover connected to a surface constructed by Hirzebruch in his works for constructing surfaces with Chern ratio equal to $3$ by arrangements of lines on the plane. Furthermore, we obtain some results that are analogous to the results of Yamasaki-Yoshida when they computed the lattice of the Hirzebruch ball quotient surface.

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