Comparing Perfect and 2nd Voronoi decompositions: the matroidal locus
arXiv:1106.3291 · doi:10.1007/s00208-011-0774-9
Abstract
We compare two rational polyhedral admissible decompositions of the cone of positive definite quadratic forms: the perfect cone decomposition and the 2nd Voronoi decomposition. We determine which cones belong to both the decompositions, thus providing a positive answer to a conjecture of V. Alexeev and A. Brunyate. As an application, we compare the two associated toroidal compactifications of the moduli space of principal polarized abelian varieties: the perfect cone compactification and the 2nd Voronoi compactification.
27 pages, 2 figures, final version, to appear in Mathematische Annalen