Some examples of algebraic surfaces with canonical map of degree 20

TL;DR

This paper constructs the first known examples of minimal algebraic surfaces of general type with a canonical map of degree 20, expanding the understanding of surface classification.

Contribution

It introduces two new minimal surfaces with specific invariants and a canonical map of degree 20, including one with a fixed part in its canonical linear system.

Findings

First examples of minimal surfaces with canonical map degree 20

Surfaces have p_g=3, q=0, K^2=20,24

One surface's canonical linear system has a non-trivial fixed part

Abstract

In this note, we construct two minimal surfaces of general type with geometric genus p_g= 3, irregularity q = 0, self-intersection of the canonical divisor K^22 =20,24 such that their canonical map is of degree 20. In one of these surfaces, the canonical linear system has a non-trivial fixed part. These surfaces, to our knowledge, are the first examples of minimal surfaces of general type with canonical map of degree 20.