On the Cohomology of the Stover Surface

ABSTRACT

We study a surface discovered by Stover which is the surface with minimal Euler number and maximal automorphism group among smooth arithmetic ball quotient surfaces. We study the natural map and discuss the problem related to the so-called Lagrangian surfaces. We obtain that this surface S has maximal Picard number and has no higher genus fibrations. We compute that its Albanese variety A is isomorphic to , for α = e^2iπ/3.

KEYWORDS:

• ball quotient surfaces
• Lagrangian surfaces
• Hurwitz ball quotients

2000 AMS SUBJECT CLASSIFICATION:

• Primary 14F35, 14J29
• Secondary 14J25, 14F45

Acknowledgments

We are grateful to Marston Conder and Derek Holt for their help in the computations of Theorem 3, and to the referee for its comments improving the readability of the article.