The cycle classes of divisorial Maroni loci

TL;DR

This paper computes the cycle classes of certain divisors in compactified Hurwitz spaces, extending the Maroni divisors, using Chern classes of vector bundles over a P^1-bundle.

Contribution

It provides a method to determine the cycle classes of divisorial Maroni loci in compactified Hurwitz spaces, extending previous results to a broader setting.

Findings

Cycle classes of effective divisors in compactified Hurwitz spaces are explicitly determined.

The approach employs Chern classes of vector bundles over a P^1-bundle.

The results extend the understanding of Maroni divisors beyond the open Hurwitz space.

Abstract

We determine the cycle classes of effective divisors in the compactified Hurwitz spaces of curves of genus g with a linear system of degree d that extend the Maroni divisors on the open Hurwitz space. Our approach uses Chern classes associated to a global-to-local evaluation map of a vector bundle over a generic $P^1$-bundle over the Hurwitz space.