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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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