On surfaces with $p_g=q=2$ and non-birational bicanonical map
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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 $K_S^2=4$.
To appear in Advances in Geometry, Latex 2e, 26 pages, title and introduction changed, minor corrections
To appear in Advances in Geometry, Latex 2e, 26 pages, title and introduction changed, minor corrections