Surfaces with $\chi =5,K^2=9$ and a canonical involution

Abstract

In this paper, we classify the minimal surfaces of general type with $\chi =5$, $K^2=9$ whose canonical map is composed with an involution. We obtain 6 families, whose dimensions in the moduli space are 28, 27, 33, 32, 31 and 32 respectively. Among them, the family of surfaces having a genus 2 fibration forms an irreducible component of ${\mathfrak{M}}_{\chi =5,K^2=9}$.

18 pages. arXiv admin note: text overlap with arXiv:math/0603094 by other authors