Moduli spaces of curves with effective r-spin structures

Details Moduli spaces of curves with effective r-spin structures Moduli spaces of curves with effective r-spin structures

2003-09-12

arxiv.org/abs/math/0309217v2

Mathematics

Algebraic Geometry

21 pages, AMSLatex, added the description of connected components of the moduli space

Scientific paper

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 $r$-spin curves consisting of $r$-spin structures $L$ such that $h^0(L)\neq 0$. Finally, we study the relation between the locus $S^0$ and Witten's virtual top Chern class.

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