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

Title & Authors
INVOLUTIONS ON SURFACES OF GENERAL TYPE WITH pg = 0 I. THE COMPOSED CASE
Shin, YongJoo;

Abstract
Let S be a minimal surface of general type with $\small{p_g(S)=q(S)=0}$ having an involution $\small{{\sigma}}$ over the field of complex numbers. It is well known that if the bicanonical map $\small{{\varphi}}$ of S is composed with $\small{{\sigma}}$, then the minimal resolution W of the quotient $\small{S/{\sigma}}$ is rational or birational to an Enriques surface. In this paper we prove that the surface W of S with $\small{K^2_S=5,6,7,8}$ having an involution $\small{{\sigma}}$ with which the bicanonical map $\small{{\varphi}}$ of S is composed is rational. This result applies in part to surfaces S with $\small{K^2_S=5}$ for which $\small{{\varphi}}$ has degree 4 and is composed with an involution $\small{{\sigma}}$. Also we list the examples available in the literature for the given $\small{K^2_S}$ and the degree of $\small{{\varphi}}$.
Keywords
involution;surface;of general type;
Language
English
Cited by
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