Brill-Noether geometry on moduli spaces of spin curves

TL;DR

This paper develops a new theoretical framework for Brill-Noether divisors on moduli spaces of stable spin curves, computing their classes and exploring the geometry of spin structures relative to Raynaud theta-divisors.

Contribution

It introduces a novel theory of Brill-Noether divisors on moduli spaces of spin curves and calculates their classes, advancing understanding of spin curve geometry.

Findings

Defined spin Brill-Noether cycles via Raynaud theta-divisors

Computed classes of Brill-Noether divisors on moduli spaces

Established geometric relations between spin structures and Jacobians

Abstract

We develop a theory of Brill-Noether divisors on the moduli space of stable spin curves of genus g, and compute the classes of these loci. A spin Brill-Noether cycle is defined in terms of the relative position of the spin structure with respect to certain Raynaud theta-divisors in the Jacobian of the curve.