The universal theta divisor over the moduli space of curves
Algebraic Geometry
2016-11-22 v4
Abstract
We carry out a complete birational classification of the universal theta divisor Th_g over the moduli space of curves of genus g, and show that Th_g enjoys good rationality properties for g<12, and is a variety of general type for g\geq 12. The key ingredient is an intersection-theoretic study of the universal antiramification locus of the Gauss map. We also present a complete classification of the universal symmetric product of degree g-2 over M_g.
Keywords
Cite
@article{arxiv.1009.0184,
title = {The universal theta divisor over the moduli space of curves},
author = {Gavril Farkas and Alessandro Verra},
journal= {arXiv preprint arXiv:1009.0184},
year = {2016}
}
Comments
17 pages. Appeared in Journal de Mathematiques Pures et Appliquees. Typo corrected in statement of Theorem 5