On the geometry of the moduli space of spin curves
Abstract
We determine the smooth locus and the locus of canonical singularities in the Cornalba compactification Sg of the moduli space Sg 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 Sg extends holomorphically to a desingularisation of Sg.
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