Related papers: Free planes in lattice sphere packings
In the category of free arrangements, inductively and recursively free arrangements are important. In particular, in the former, the conjecture by Terao asserting that freeness depends only on combinatorics holds true. A long standing…
Let $R$ be a real smooth affine domain of dimension $3$ such that $R$ has either no real maximal ideals or the intersection of all real maximal ideals in $R$ has height at least $1$. Then we prove that all stably free $R$-modules of rank…
Let $C$ be a reduced complex projective plane curve, and let $d_1$ and $d_2$ be the first two smallest exponents of $C$. For a free curve $C$ of degree $d$, there is a simple formula relating $d,d_1, d_2$ and the total Tjurina number of…
We show that up to unimodular equivalence there are only finitely many d-dimensional lattice polytopes without interior lattice points that do not admit a lattice projection onto a (d-1)-dimensional lattice polytope without interior lattice…
We present a method to quantize free fermions which eliminates the doublers when implemented on the lattice in any number of dimensions and in the $m=0$ limit. The elimination of doublers is achieved by combining a second-order description…
We consider zero temperature packings of soft spheres, that undergo a jamming to unjamming transition as a function of packing fraction. We compare differences in the structure, as measured from the contact statistics, of a finite subsystem…
In this paper we will first introduce the notion of affine structures on a ringed space and then obtain several properties. Affine structures on a ringed space, arising mainly from complex analytical spaces of algebraic schemes over number…
A lattice approach is developed to measure the sphaleron free energy. Its feasibility is demonstrated through a Monte Carlo study of the two-dimensional O(3) sigma model.
Two types of particles, A and B with their corresponding antiparticles, are defined in a one dimensional cyclic lattice with an odd number of sites. In each step of time evolution, each particle acts as a source for the polarization field…
This article provides, over any field, infinitely many algebraic embeddings of the affine spaces $\mathbb{A}^1$ and $\mathbb{A}^2$ into smooth quadrics of dimension two and three respectively, which are pairwise non-equivalent under…
We study limit shapes for dimer models on domains of the hexagonal lattice with free boundary conditions. This is equivalent to the large deviation phenomenon for a random stepped surface over domains fixed only at part of the boundary.
We develop a model to describe the properties of random assemblies of polydisperse hard spheres. We show that the key features to describe the system are (i) the dependence between the free volume of a sphere and the various coordination…
We consider dimer model on a hexagonal lattice. This model can be seen as a "pile of cubes in the box". The energy of configuration is given by the volume of the pile and the partition function is computed by the classical MacMahon formula…
We construct an infinite family of knots in rational homology spheres with irreducible, non-fibered complements, for which every non-longitudinal filling is an L-space.
Given a family of complex affine planes, we show that it is trivial over a Zariski open subset of the base. The proof relies upon a relative version of the contraction theorem.
Inversive geometry can be used to generate exactly self-similar space-filling sphere packings. We present a construction method in two dimensions and generalize it to search for packings in higher dimensions. We newly discover 29…
Determining the space of free discrete two generator groups of M\"obius transformations is an old and difficult problem. In this paper we show how to construct large balls of full dimension in this space. To do this, we begin with a marked…
Each labeled rooted tree is associated with a hyperplane arrangement, which is free with exponents given by the depths of the vertices of this tree. The intersection lattices of these arrangements are described through posets of forests.…
There are exactly two different types of bi-dimensional improper affine spheres: the non-convex ones can be modeled by the center-chord transform of a pair of planar curves while the convex ones can be modeled by a holomorphic map. In this…
We classify all regular three-dimensional convex cones which possess an automorphism group of dimension at least two, and provide analytic expressions for the complete hyperbolic affine spheres which are asymptotic to the boundaries of…