Comparing Perfect and 2nd Voronoi decompositions: the matroidal locus
Combinatorics
2012-11-12 v2 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.1106.3291,
title = {Comparing Perfect and 2nd Voronoi decompositions: the matroidal locus},
author = {Margarida Melo and Filippo Viviani},
journal= {arXiv preprint arXiv:1106.3291},
year = {2012}
}
Comments
27 pages, 2 figures, final version, to appear in Mathematische Annalen