The strong Franchetta Conjecture in arbitrary characteristics

Details The strong Franchetta Conjecture in arbitrary characteristics The strong Franchetta Conjecture in arbitrary characteristics

2002-03-19

arxiv.org/abs/math/0203186v3

Internat. J. Math. 14 (2003), 371-396

Mathematics

Algebraic Geometry

23 pages, major extension, to appear in Internat. J. Math

Scientific paper

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.

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