Some surfaces with canonical map of degree 4

TL;DR

This paper constructs infinite families of minimal surfaces of general type with a canonical map of degree 4, exploring the range of their slope limits which vary within a specific interval.

Contribution

It introduces unbounded families of such surfaces and analyzes the possible limit values of their slopes, expanding understanding of their geometric properties.

Findings

Constructed unbounded families of surfaces with canonical map degree 4.

Identified that the slopes' limits can take countably many values between 6+2/3 and 8.

Demonstrated the variability of slope limits in these families.

Abstract

In this short note we construct unbounded families of minimal surfaces of general type with canonical map of degree 4 such that the limits of the slopes assume countably many different values among 6+2/3 and 8.