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

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 $2$.

Final version. To appear in IMRN

References in corpus (3)

• A family of surfaces with $p_g=q=2,K^2=7$ and Albanese map of degree $3$
• Explicit Schoen surfaces
• Involutions on surfaces with $p_g=q=1$

Cited by in corpus (2)

• Monodromy representations and surfaces with maximal Albanese dimension
• Rigidity of modular morphisms via Fujita decomposition