Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



On the geometry of the moduli space of spin curves

Author: Katharina Ludwig
Journal: J. Algebraic Geom. 19 (2010), 133-171
Published electronically: April 23, 2009
MathSciNet review: 2551759
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Abstract: We determine the smooth locus and the locus of canonical singularities in the Cornalba compactification $ \overline{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 $ \overline{S}_g$ extends holomorphically to a desingularisation of $ \overline{S}_g$.

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Katharina Ludwig
Affiliation: Institut für Algebraische Geometrie, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany

Received by editor(s): August 2, 2007
Received by editor(s) in revised form: October 18, 2007
Published electronically: April 23, 2009

Journal of Algebraic Geometry
The Journal of Algebraic Geometry
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