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

Ciro Ciliberto; Margarida Mendes Lopes

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

Algebraic Geometry 2007-05-23 v2

Authors: Ciro Ciliberto , Margarida Mendes Lopes

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 $(A,\Theta)$ , with $\Theta$ irreducible. The double cover $S\to A$ is branched along a divisor $B\in |2\Theta|$ , having at most double points and so $K_S^2=4$ .

Keywords

algebraic surfaces general type bicanonical map abelian surface double cover pluricanonical systems

Cite

@article{arxiv.math/0012211,
  title  = {On surfaces with $p_g=q=2$ and non-birational bicanonical map},
  author = {Ciro Ciliberto and Margarida Mendes Lopes},
  journal= {arXiv preprint arXiv:math/0012211},
  year   = {2007}
}

Comments

To appear in Advances in Geometry, Latex 2e, 26 pages, title and introduction changed, minor corrections

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

Abstract

Keywords

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