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Perfect forms and the moduli space of abelian varieties

N. I. Shepherd-Barron
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Abstract

Perfect quadratic forms give a toroidal compactification of the moduli space of principally polarized abelian g-folds that is Q-factorial and whose ample classes are characterized, over any base. In characteristic zero it has canonical singularities if g is at least 5, and is the canonical model (in the sense of Mori and Reid) if g is at least 12.

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N. I. Shepherd-Barron. 2005-02-16. Perfect forms and the moduli space of abelian varieties. https://doi.org/10.1007/s00222-005-0453-0

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