Nef Divisors on Moduli Spaces of Abelian Varieties
Abstract
Description
We determine the cone of nef divisors on the Voronoi compactification A_g^* of the moduli space A_g of principally polarized abelian varieties of dimension g for genus g=2,3. As a corollary we obtain that the spaces A_g^*(n) with level-n structure are a minimal, resp. canonical, model for g=2, n>=4, resp. n>=5 and g=3, n>=3, resp. n>=4. We give two proofs: The easy and quick one reduces the problem to \bar M_g where we can use a result of Faber. This approach cannot be generalized to higher genus g. The main point of the paper is, therefore, to give a second proof using theta functions and a result of Weissauer. This technique can be at least partially generalized to higher genus. We formulate a conjecture for the nef cone of A_g^* for all g.
LaTeX2e, 23 pages. The proof of the main result has been shortened. In particular, the former technical propositions 4.3 and 4.4 were replaced by a simpler argument
LaTeX2e, 23 pages. The proof of the main result has been shortened. In particular, the former technical propositions 4.3 and 4.4 were replaced by a simpler argument