# The strong Franchetta Conjecture in arbitrary characteristics

Research paper by Stefan Schroeer

Indexed on: 06 Feb '03Published on: 06 Feb '03Published in: Mathematics - Algebraic Geometry

#### 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.