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arXiv · 1410.8657

On the cohomology of Stover Surface

Amir Džambić·Xavier Roulleau
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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 $\alpha=e^{2i\pi/3}$.

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Amir Džambić, Xavier Roulleau. 2014-10-31. On the cohomology of Stover Surface. https://arxiv.org/abs/1410.8657

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