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arXiv · 0805.4513

Involutions on surfaces with $p_g=q=1$

Carlos Rito
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Abstract

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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Carlos Rito. 2008-05-29. Involutions on surfaces with $p_g=q=1$. https://arxiv.org/abs/0805.4513

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