The classification of universal Jacobians over the moduli space of curves
Algebraic Geometry
2013-10-21 v2
Abstract
We carry out a complete birational classification of the degree g universal Jacobian P_g over the moduli space of curves, highlighting the transition cases g=10, 11. The universal Jacobian is unirational when g<10, has Kodaira dimension zero for g=10 and Kodaira dimension 19 for g=11. For g>11, the variety P_g has Kodaira dimension 3g-3, that is, the maximum allowed by Iitaka's easy addition formula for fibre spaces. In particular, we disprove the expectation that P_g and M_g have the same Kodaira dimension for all genera.
Keywords
Cite
@article{arxiv.1005.5354,
title = {The classification of universal Jacobians over the moduli space of curves},
author = {Gavril Farkas and Alessandro Verra},
journal= {arXiv preprint arXiv:1005.5354},
year = {2013}
}
Comments
19 pages. Final version, to appear in Comm. Math. Helvetici