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On the cohomology of the Stover surface. (English) Zbl 1375.14082
Summary: 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 $$\bigwedge^2H^1(S,\mathcal{C})\to H^2(S,\mathcal{C})$$ 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 $$(\mathcal{C}/\mathbb{Z}[\alpha])^7$$, for $$\alpha=e^{2i\pi/3}$$.

##### MSC:
 14F35 Homotopy theory and fundamental groups in algebraic geometry 14J29 Surfaces of general type 14J25 Special surfaces 14F45 Topological properties in algebraic geometry
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