Nef Divisors on Moduli Spaces of Abelian Varieties

Details Nef Divisors on Moduli Spaces of Abelian Varieties Nef Divisors on Moduli Spaces of Abelian Varieties

1997-08-19

arxiv.org/abs/alg-geom/9708016v2

Mathematics

Algebraic Geometry

LaTeX2e, 23 pages. The proof of the main result has been shortened. In particular, the former technical propositions 4.3 and 4

Scientific paper

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.

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