A compactification of the moduli space of multiple-spin curves

Abstract

We construct a smooth Deligne-Mumford compactification for the moduli space of curves with an m-tuple of spin structures using line bundles on quasi-stable curves as limiting objects, as opposed to line bundles on stacky curves. For all m, we give a combinatorial description of the local structure of the corresponding coarse moduli spaces. We also classify all irreducible and connected components of the resulting moduli spaces of multiple-spin curves.

Published version. 31 pages. 2 Figures. Revised and expanded Section 7 which classifies the components of the moduli space of multiple-spin curves

References in corpus (2)

• Prym varieties of genus four curves
• Effective reconstruction of generic genus 5 curves from their theta hyperplanes