8 citations · 20 across the 10 of their papers we have counts for
12 papers
Moduli of polarized Enriques surfaces -- computational aspects
Mathieu Dutour Sikirić, Klaus Hulek
Moduli spaces of (polarized) Enriques surfaces can be described as open subsets of modular varieties of orthogonal type. It was shown by Gritsenko and Hulek that there are, up to i…
Extreme Divisors on and Differences over Characteristic 2
Mathieu Dutour Sikirić, Eric Jovinelly
We find 101,052 new extreme divisors on (in 31 -orbits) and millions of extreme nef curves over characteristic 0. Over characteristic 2, we identify two more $…
Iso Edge Domains
Mathieu Dutour Sikirić, Mario Kummer
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 dime…
A variation on the Rubik's cube
Mathieu Dutour Sikirić
The Rubik's cube is a famous puzzle in which faces can be moved and the corresponding movement operations define a group. We consider here a generalization to any -valent map. W…
A Canonical Form for Positive Definite Matrices
Mathieu Dutour Sikirić, Anna Haensch, John Voight +1
We exhibit an explicit, deterministic algorithm for finding a canonical form for a positive definite matrix under unimodular integral transformations. We use characteristic sets of…
Voronoi complexes in higher dimensions, cohomology of for and the triviality of
Mathieu Dutour Sikirić, Philippe Elbaz-Vincent, Alexander Kupers +1
We enumerate the low dimensional cells in the Voronoi cell complexes attached to the modular groups and for , using quotient sublattices techniques…
On the Voronoi Conjecture for combinatorially Voronoi parallelohedra in dimension five
Mathieu Dutour Sikirić, Alexey Garber, Alexander Magazinov
In a recent paper Garber, Gavrilyuk and Magazinov proposed a sufficient combinatorial condition for a parallelohedron to be affinely Voronoi. We show that this condition holds for…
Periodic triangulations of
Mathieu Dutour Sikirić, Alexey Garber
We consider in this work triangulations of that are periodic along . They generalize the triangulations obtained from Delaunay tessellations of lattice…
Rational factorizations of completely positive matrices
Mathieu Dutour Sikirić, Achill Schürmann, Frank Vallentin
In this note it is proved that every rational matrix which lies in the interior of the cone of completely positive matrices also has a rational cp-factorization.
The hypermetric cone on vertices and some generalizations
Michel Deza, Mathieu Dutour Sikirić
The lists of facets -- in orbits -- and of extreme rays -- in orbits -- of the hypermetric cone are computed. The first generalization…
Smoothness and singularities of the perfect form and the second Voronoi compactification of
Mathieu Dutour Sikirić, Klaus Hulek, Achill Schürmann
We study the cones in the first Voronoi or perfect cone decomposition of quadratic forms with respect to the question which of these cones are basic or simplicial. As a consequence…
The special cuts of 600-cell
Mathieu Dutour Sikirić, Wendy Myrvold
A polytope is called {\em regular-faced} if every one of its facets is a regular polytope. The 4-dimensional regular-faced polytopes were determined by G. Blind and R. Blind \cite{…