Divisors on Hurwitz spaces: an appendix to 'The cycle classes of divisorial Maroni loci'

TL;DR

This paper constructs a new stratification on Hurwitz spaces similar to the Maroni stratification, which forms a divisor for almost all pairs (d,g), and computes its divisor class on the compactified space.

Contribution

It introduces a generalized stratification on Hurwitz spaces that exists as a divisor for nearly all (d,g) pairs, extending previous Maroni stratification results.

Findings

Constructed a new stratification analogous to Maroni stratification.

Established conditions under which the stratification forms a divisor.

Calculated the divisor class on the compactified Hurwitz space.

Abstract

The Maroni stratification on the Hurwitz space of degree $d$ covers of genus $g$ has a stratum that is a divisor only if $d-1$ divides $g$. Here we construct a stratification on the Hurwitz space that is analogous to the Maroni stratification, but has a divisor for all pairs $(d,g)$ with $d \leq g$ with a few exceptions and we calculate the divisor class of an extension of these divisors to the compactified Hurwitz space.