Involutions on surfaces with $p_g=q=1$

Details Involutions on surfaces with $p_g=q=1$ Involutions on surfaces with $p_g=q=1$

2008-05-29

arxiv.org/abs/0805.4513v1

Mathematics

Algebraic Geometry

34 pages

Scientific paper

In this paper some numerical restrictions for surfaces with an involution are obtained. These formulas are used to study surfaces of general type $S$ with $p_g=q=1$ having an involution $i$ such that $S/i$ is a non-ruled surface and such that the bicanonical map of $S$ is not composed with $i.$ A complete list of possibilities is given and several new examples are constructed, as bidouble covers of surfaces. In particular the first example of a minimal surface of general type with $p_g=q=1$ and $K^2=7$ having birational bicanonical map is obtained.

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