On the geometry of the moduli space of spin curves

Details On the geometry of the moduli space of spin curves On the geometry of the moduli space of spin curves

2007-07-12

arxiv.org/abs/0707.1831v1

Mathematics

Algebraic Geometry

PDFLaTeX, 36 pages, 28 figures

Scientific paper

We determine the smooth locus and the locus of canonical singularities in the Cornalba compactification \bar S_g of the moduli space S_g of spin curves, i.e., smooth curves of genus g with a theta characteristic. Moreover, the following lifting result for pluricanonical forms is proved: Every pluricanonical form on the smooth locus of \bar S_g extends holomorphically to a desingularisation of \bar S_g.

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