The strong Franchetta Conjecture in arbitrary characteristics
Algebraic Geometry
2007-05-23 v3
Abstract
Using Moriwaki's calculation of the Q-Picard group for the moduli space of curves, I prove the strong Franchetta Conjecture in all characteristics. That is, the canonical class generates the group of rational points on the Picard scheme for the generic curve of genus g>2. Similar results hold for generic pointed curves. Moreover, I show that Hilbert's Irreducibility Theorem implies that there are many other nonclosed points in the moduli space of curves with such properties.
Cite
@article{arxiv.math/0203186,
title = {The strong Franchetta Conjecture in arbitrary characteristics},
author = {Stefan Schroeer},
journal= {arXiv preprint arXiv:math/0203186},
year = {2007}
}
Comments
23 pages, major extension, to appear in Internat. J. Math