Effective divisors on Hurwitz spaces

TL;DR

This paper demonstrates the effectiveness of the canonical bundle on certain Hurwitz spaces, specifically those parametrizing degree k covers of the projective line from curves with genus between 13 and 20.

Contribution

It establishes the effectiveness of the canonical bundle on Hurwitz spaces for a range of genera, advancing understanding of their geometric properties.

Findings

Canonical bundle is effective for specified Hurwitz spaces.

Results apply to covers of degree k from genus 13 to 20.

Enhances knowledge of the geometry of Hurwitz spaces.

Abstract

We prove the effectiveness of the canonical bundle of several Hurwitz spaces of degree k covers of the projective line from curves of genus 13<g<20.