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arXiv · 1106.3291

Comparing Perfect and 2nd Voronoi decompositions: the matroidal locus

Margarida Melo·Filippo Viviani
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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.

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Margarida Melo, Filippo Viviani. 2011-12-09. Comparing Perfect and 2nd Voronoi decompositions: the matroidal locus. https://doi.org/10.1007/s00208-011-0774-9

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