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

2000/12/21 by Ciro Ciliberto, Ciliberto, Ciro, Margarida Mendes Lopes +1
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.math/0012211

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

arxiv created 2001/12/05 · arxiv updated 2009/11/30

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→ A is branched along a divisor B∈ |2Θ|, having at most double points and so K_S²=4.

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