Syzygy divisors on Hurwitz spaces

TL;DR

This paper introduces a sequence of effective divisors on Hurwitz spaces derived from syzygy vector bundles, computes their cycle classes, and finds they are proportional, advancing understanding of the geometry of these moduli spaces.

Contribution

It constructs and analyzes a new family of divisors on Hurwitz spaces using syzygy bundles, providing explicit cycle class calculations and revealing proportionality among them.

Findings

Cycle classes of the divisors are proportional.

Divisors are constructed from syzygy vector bundles.

Results enhance understanding of Hurwitz space geometry.

Abstract

We describe a sequence of effective divisors on the Hurwitz space $H_{d,g}$ for $d$ dividing $g-1$ and compute their cycle classes on a partial compactification. These divisors arise from vector bundles of syzygies canonically associated to a branched cover. We find that the cycle classes are all proportional to each other.