Z/rZ-equivariant covers of P^1 with moving ramification

TL;DR

This paper provides a simple formula for counting equivariant meromorphic functions on cyclic covers of P^1 with moving ramification points, generalizing previous results and offering a new proof for specific hyperelliptic cases.

Contribution

It introduces a new, straightforward formula for equivariant meromorphic functions on cyclic covers with variable ramification, extending prior work and simplifying proofs.

Findings

Derived a formula for equivariant meromorphic functions with moving ramification

Generalized previous results on hyperelliptic odd covers

Provided a new proof for existing theorems in the field

Abstract

Let X -> P^1 be a general cyclic cover. We give a simple formula for the number of equivariant meromorphic functions on X subject to ramification conditions at variable points. This generalizes and gives a new proof of a recent result of the second author and Pirola on hyperelliptic odd covers.