152 research outputs found
New results on torus cube packings and tilings
We consider sequential random packing of integral translate of cubes
into the torus . Two special cases are of special
interest:
(i) The case which corresponds to a discrete case of tilings
(considered in \cite{cubetiling,book})
(ii) The case corresponds to a case of continuous tilings
(considered in \cite{combincubepack,book})
Both cases correspond to some special combinatorial structure and we describe
here new developments.Comment: 5 pages, conference pape
Moduli of polarised Enriques surfaces — Computational aspects
Moduli spaces of (polarised) 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 isomorphism, only finitely many different moduli spaces of polarised Enriques surfaces. Here, we investigate the possible arithmetic groups and show that there are exactly 87 such groups up to conjugacy. We also show that all moduli spaces are dominated by a moduli space of polarised Enriques surfaces of degree 1240. Ciliberto, Dedieu, Galati and Knutsen have also investigated moduli spaces of polarised Enriques surfaces in detail. We discuss how our enumeration relates to theirs. We further compute the Tits building of the groups in question. Our computation is based on groups and indefinite quadratic forms and the algorithms used are explained
Iso Edge Domains
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 .
In this work we revisit this decomposition and prove the following new
results:
We review the existing theory and give a general mass-formula for
the iso-edge domains.
We prove that the associated toroidal compactification of the
moduli space of principally polarized abelian varieties is projective.
We prove the Conway--Sloane conjecture in dimension .
We prove that the quadratic forms for which the conorms are
non-negative are exactly the matroidal ones in dimension
- …