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

Author: Xavier Roulleau
Journal: Proc. Amer. Math. Soc. 139 (2011), 3405-3412
MSC (2010): Primary 14J29; Secondary 14J25, 22E40
Published electronically: February 18, 2011
MathSciNet review: 2813372
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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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Additional Information

Xavier Roulleau
Affiliation: Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8914, Japan

Keywords: Algebraic surfaces, ball lattices, orbifolds, Fano surfaces of cubic threefolds, degree 5 del Pezzo surface.
Received by editor(s): September 23, 2008
Received by editor(s) in revised form: September 15, 2009, and August 24, 2010
Published electronically: February 18, 2011
Communicated by: Ted Chinburg
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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