A Note on a Brill-Noether Locus over a Non-hyperelliptic curve of genus 4

TL;DR

This paper investigates a specific Brill-Noether locus on a non-hyperelliptic genus 4 curve, establishing an isomorphism to the Donagi-Izadi cubic threefold under a particular trigonal line bundle condition.

Contribution

It demonstrates an isomorphism between a Brill-Noether locus and the Donagi-Izadi cubic threefold for certain trigonal line bundles on genus 4 curves.

Findings

Brill-Noether locus is isomorphic to Donagi-Izadi cubic threefold

The isomorphism holds when the pencils of two trigonal line bundles coincide

Provides geometric insight into the structure of special loci on genus 4 curves

Abstract

We prove that a certain Brill-Noether locus over a non-hyperelliptic curve $C$ of genus 4, is isomorphic to the \textit{Donagi-Izadi cubic threefold} in the case when the pencils of the two trigonal line bundles of $C$ coincide.