Examples of surfaces with canonical maps of degree 12, 13, 15, 16 and 18

Abstract

In this note, we present examples of complex algebraic surfaces with canonical maps of degree 12, 13, 15, 16 and 18. They are constructed as quotients of a product of two curves of genus 10 and 19 using certain non-free actions of the group $$S_3\times {\mathbb {Z}}_3^2$$ S 3 × Z 3 2 . To our knowledge, there are no other examples in the literature of surfaces with canonical map of degree 13, 15 and 18.