Iso Edge Domains
2021
Iso-edge domains are a variant of the iso-Delaunay decomposition introduced by Voronoi. They were introduced by Baranovskii & Ryshkov in order to solve the covering problem in dimension $5$.
In this work we revisit this decomposition and prove the following new results:
$\bullet$ We review the existing theory and give a general mass-formula for the iso-edge domains.
$\bullet$ We prove that the associated toroidal compactification of the moduli space of principally polarized abelian varieties is projective.
$\bullet$ We prove the Conway--Sloane conjecture in dimension $5$.
$\bullet$ We prove that the quadratic forms for which the conorms are non-negative are exactly the matroidal ones in dimension $5$.
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