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

Xavier Roulleau
2011 Proceedings of the American Mathematical Society  
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
more » ... , we obtain some results that are analogous to the results of Yamasaki-Yoshida when they computed the lattice of the Hirzebruch ball quotient surface. c 2 equals 3 have been constructed algebraically, i.e. by ramified covers of known surfaces. The first examples are owed
doi:10.1090/s0002-9939-2011-10847-5 fatcat:ceytsnlgijc4fh4vm52jvzsnxy