On the cohomology of 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 ${\wedge }^2{H}^1(S,\mathbb{C})\to H^2(S,\mathbb{C})$ and we 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 $(\mathbb{C}/\mathbb{Z}[\alpha ]{)}^7$, for $\alpha =e^{2i\pi /3}$.

7 pages, Comments welcome