Moduli spaces of curves with effective r-spin structures

2003/09/12 by Polishchuk, Alexander
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0309217

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 S⁰ in the moduli space of r-spin curves consisting of r-spin structures L such that h⁰(L)≠ 0. Finally, we study the relation between the locus S⁰ and Witten's virtual top Chern class.

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