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http://dx.doi.org/10.4134/CKMS.2013.28.3.425

INVOLUTIONS ON SURFACES OF GENERAL TYPE WITH pg = 0 I. THE COMPOSED CASE  

Shin, YongJoo (Department of Mathematics Sogang University)
Publication Information
Communications of the Korean Mathematical Society / v.28, no.3, 2013 , pp. 425-432 More about this Journal
Abstract
Let S be a minimal surface of general type with $p_g(S)=q(S)=0$ having an involution ${\sigma}$ over the field of complex numbers. It is well known that if the bicanonical map ${\varphi}$ of S is composed with ${\sigma}$, then the minimal resolution W of the quotient $S/{\sigma}$ is rational or birational to an Enriques surface. In this paper we prove that the surface W of S with $K^2_S=5,6,7,8$ having an involution ${\sigma}$ with which the bicanonical map ${\varphi}$ of S is composed is rational. This result applies in part to surfaces S with $K^2_S=5$ for which ${\varphi}$ has degree 4 and is composed with an involution ${\sigma}$. Also we list the examples available in the literature for the given $K^2_S$ and the degree of ${\varphi}$.
Keywords
involution; surface; of general type;
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