On modular properties of odd theta-characteristics
Abstract
Description
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.
13 pages. To appear on the AMS Contemporary Mathematics volume "Advances in Algebraic Geometry Motivated by Physics"
13 pages. To appear on the AMS Contemporary Mathematics volume "Advances in Algebraic Geometry Motivated by Physics"