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On surfaces with $p_g=q=2$ and non-birational bicanonical map

Ciro Ciliberto·Margarida Mendes Lopes
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Abstract

This paper is devoted to the classification of irregular surfaces of general type with $p_g=q=2$ and non birational bicanonical map. The main result is that, if $S$ is such a surface and if $S$ is minimal with no pencil of curves of genus 2, then $S$ is a double cover of a principally polarized abelian surface $(A,Θ)$, with $Θ$ irreducible. The double cover $S\to A$ is branched along a divisor $B\in |2Θ|$, having at most double points and so $K_S^2=4$.

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BibTeXRIS

Ciro Ciliberto, Margarida Mendes Lopes. 2001-12-05. On surfaces with $p_g=q=2$ and non-birational bicanonical map. https://arxiv.org/abs/math/0012211

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