Moduli spaces of curves with effective r-spin structures

الأصل · EN

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.