Perfect forms and the moduli space of abelian varieties

@article{Shepherdbarron2006PerfectFA,
  title={Perfect forms and the moduli space of abelian varieties},
  author={N. I. Shepherd-barron},
  journal={Inventiones mathematicae},
  year={2006},
  volume={163},
  pages={25-45}
}
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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