2002/03/31 by Stefan Schroeer
Mathematics · #math.AG #msc:14G05 #msc:14H10 #msc:14H40 #msc:14K15
published as Internat. J. Math. 14 (2003), 371-396 · 23 pages, major extension, to appear in Internat. J. Math
arxiv created 2003/02/06 · arxiv updated 2009/11/30
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.