Uniruledness of Some Moduli Spaces of Pointed Spin Curves

TL;DR

This paper proves that certain moduli spaces of pointed spin curves are uniruled for specific genera and numbers of marked points, advancing understanding of their geometric properties.

Contribution

It establishes the uniruledness of $\

Findings

Proves $\\mathcal{S}_{g, 2}$ is uniruled for some $g$

Proves $\\mathcal{S}_{g, 4}$ is uniruled for some $g$

Proves $\\mathcal{S}_{g, 6}$ is uniruled for some $g$

Abstract

The moduli space $\mathcal{S}_{g, 2n}$ parametrizes pointed curves with spin structure. We prove that $\mathcal{S}_{g, 2}$, $\mathcal{S}_{g, 4}$ and $\mathcal{S}_{g, 6}$ are uniruled for particular values of $g$.