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 S ¯ g \overline {S}_g of the moduli space S g S_g of spin curves, i.e., smooth curves of genus g g with a theta characteristic. Moreover, the following lifting result for pluricanonical forms is proved: Every pluricanonical form on the smooth locus of S ¯ g \overline {S}_g extends holomorphically to a desingularisation of S ¯ g \overline {S}_g .