Moduli spaces of curves with effective r-spin structures

Abstract

We introduce the moduli stack of pointed curves equipped with effective $r$-spin structures: these are effective divisors $D$ such that $rD$ is a canonical divisor modified at marked points. We prove that this moduli space is smooth and compute its dimension. We also prove that it always contains a component that projects birationally to the locus $S^0$ in the moduli space of $r$