English

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.

Keywords

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

R2 v1 2026-07-22T16:44:02.654Z