Some surfaces with canonical maps of degree $10$, $11$ and $14$

TL;DR

This paper constructs examples of complex algebraic surfaces with canonical maps of degrees 10, 11, and 14, expanding the known range of such surfaces by using quotients of Fermat septics with specific group actions.

Contribution

It introduces new examples of surfaces of general type with canonical map degrees 10, 11, and 14, constructed via quotients of Fermat septics with group actions.

Findings

Examples of surfaces with canonical maps of degrees 10, 11, and 14.

Surfaces constructed as quotients of Fermat septics.

Use of free actions of _7^2 group.

Abstract

In this note we present examples of complex algebraic surfaces of general type with canonical maps of degree $10$, $11$ and $14$. They are constructed as quotients of a product of two Fermat septics using certain free actions of the group $\mathbb Z_7^2$.