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arXiv · 1703.10646

A pair of rigid surfaces with $p_g=q=2$ and $K^2=8$ whose universal cover is not the bidisk

Francesco Polizzi·Carlos Rito·Xavier Roulleau
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Abstract

We construct two complex-conjugated rigid surfaces with $p_g=q=2$ and $K^2=8$ whose universal cover is not biholomorphic to the bidisk. We show that these are the unique surfaces with these invariants and Albanese map of degree $2$, apart the family of product-quotient surfaces constructed by Penegini. This completes the classification of surfaces with $p_g=q=2, K^2=8$ and Albanese map of degree $2$.

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Francesco Polizzi, Carlos Rito, Xavier Roulleau. 2018-04-30. A pair of rigid surfaces with $p_g=q=2$ and $K^2=8$ whose universal cover is not the bidisk. https://doi.org/10.1093/imrn%2Frny107

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