On modular properties of odd theta-characteristics

Details On modular properties of odd theta-characteristics On modular properties of odd theta-characteristics

2000-11-21

arxiv.org/abs/math/0011154v1

Mathematics

Algebraic Geometry

13 pages. To appear on the AMS Contemporary Mathematics volume "Advances in Algebraic Geometry Motivated by Physics"

Scientific paper

A general canonical curve X determines a finite set T(X) of hyperplanes, which is in bijective correspondence with the set of odd theta-characteristics of X. The definition of T(X) can be extended to certain singular curves, in a way that is compatible with degenerations. If X is a Deligne-Mumford stable curve (or a cuspidal curve), we describe the enumerative and local geometry of T(X); this is applied to show that some singular curves are uniquely determined by T(X). This work generalizes the preliminary steps used in AG/0008239 (with E. Sernesi) to show that a general curve of genus 3 can be recovered from its odd theta-characteristics.

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