Related papers: Abelian sandpiles and algebraic models
We describe algebraically defined cohomological and homological Albanese and Picard 1-motives (or mixed motives) of any algebraic variety in characteristic zero, generalizing the classical Albanese and Picard varieties. We compute Hodge,…
Consider the algebraic function $\Phi_{g,n}$ that assigns to a general $g$-dimensional abelian variety an $n$-torsion point. A question first posed by Kronecker and Klein asks: What is the minimal $d$ such that, after a rational change of…
In this paper we study a relationship between elementary equivalence of endomorphism rings of Abelian p-groups and second order equivalence of the corresponding Abelian p-groups.
We show a case of Zilber's Exponential-Algebraic Closedness Conjecture, establishing that the conjecture holds for varieties which split as the product of a linear subspace of the additive group $\mathbb{C}^n$ and an algebraic subvariety of…
Motivated by a recent conjecture of Zabrocki, Wallach described the alternants in the super-coinvariant algebra of the symmetric group in one set of commuting and one set of anti-commuting variables under the diagonal action. We give a…
We present an algorithm for determining all inequivalent abelian symmetries of non-degenerate quasi-homogeneous polynomials and apply it to the recently constructed complete set of Landau--Ginzburg potentials for $N=2$ superconformal field…
Polymer systems in slab geometries are studied on the basis of the recently presented Gaussian Ellipsoid Model [J. Chem. Phys. 114, 7655 (2001)].The potential of the confining walls has an exponential shape. For homogeneous systems in…
We study critical properties of the continuous Abelian sandpile model with anisotropies in toppling rules that produce ordered patterns on it. Also we consider the continuous directed sandpile model perturbed by a weak quenched randomness…
We construct two quantum spin chains Hamiltonians with quantum sl(2|1) invariance. These spin chains define variants of the Hubbard model and describe electron models with pair hoppings. A cubic algebra that admits the Birman-Wenzl-Murakami…
There is a commutative algebra of differential-difference operators, with two parameters, associated to any dihedral group with an even number of reflections. The intertwining operator relates this algebra to the algebra of partial…
A method is proposed for the characterisation of the entropy of cellular structures, based on the compactivity concept for granular packings. Hamiltonian-like volume functions are constructed both in two and in three dimensions, enabling…
This paper is concerned with Wilmes' conjecture regarding abelian sandpile models. We introduce the concept of boundary divisors and use this to prove the conjecture for the first Betti number. Further results suggest that this method could…
A classification, according to invariant theory, of non-constant invariant Abel ODEs known as solvable and found in the literature is presented. A set of new integrable classes depending on one or no parameters, derived from the analysis of…
We introduce a notion of ellipticity of complexes of linear pseudodifferential operators acting on sections of $A$-Hilbert bundles over smooth manifolds, $A$ being a $C^*$-algebra. We prove that the cohomology groups of an $A$-elliptic…
Let $F:\mathbb Z^2\to \mathbb Z$ be the pointwise minimum of several linear functions. The theory of smoothing of integer-valued superharmonic function allows us to prove that under certain conditions there exists the pointwise minimal…
We estimate the fraction of isogeny classes of abelian varieties over a finite field which have a given characteristic polynomial P(T) modulo l. As an application we find the proportion of isogeny classes of abelian varieties with a…
We develop some basic results about full amalgamation classes with intrinsic trascendentals. These classes have generics whose models may have finite subsets whose intrinsic closure is not contained in its algebraic closure. We will show…
It is well-known that degree two finite field extensions can be equipped with a Hermitian-like structure similar to the extension of the complex field over the reals. In this contribution, using this structure, we develop a modular…
Non-abelian discrete symmetries are of particular importance in model building. They are mainly invoked to explain the various fermion mass hierarchies and forbid dangerous superpotential terms. In string models they are usually associated…
Let k be an algebraically closed field of characteristic zero, F its algebraically closed extension, and G be the group of k-automorphisms of F endowed with a natural topology. One of the purposes of this paper is to show that any…