Some unlimited families of minimal surfaces of general type with the canonical map of degree 8

TL;DR

This paper constructs nine new families of complex minimal surfaces of general type with a canonical map of degree 8, some with fixed parts in their canonical systems, expanding the known examples in algebraic geometry.

Contribution

It introduces nine new families of minimal surfaces with specific canonical map degrees, including cases with fixed parts, advancing the classification of such surfaces.

Findings

Nine families of surfaces constructed with canonical map degree 8

Six families have canonical systems with non-trivial fixed parts

Surfaces have irregularity 0 or 1

Abstract

In this note, we construct nine families of projective complex minimal surfaces of general type having the canonical map of degree 8 and irregularity 0 or 1. For six of these families the canonical system has a non trivial fixed part.