The geometry of the moduli space of odd spin curves
Algebraic Geometry
2014-08-20 v2
Abstract
We describe the birational geometry of the moduli space S_g^{-} of odd spin curves (theta-characteristics) for all genera g. The odd spin moduli space is a uniruled variety for g<12, and of general type for g at least 12. Furthermore, for g<9 we use the existence of Mukai models of the moduli space of curves, to prove that S_g^{-} is unirational. Our results show that in genus 8, the odd spin moduli space in unirational, whereas its even counterpart is of Calabi-Yau type.
Keywords
Cite
@article{arxiv.1004.0278,
title = {The geometry of the moduli space of odd spin curves},
author = {Gavril Farkas and Alessandro Verra},
journal= {arXiv preprint arXiv:1004.0278},
year = {2014}
}
Comments
34 pages. Final version, to appear in the Annals of Mathematics