Related papers: The separation properties for closures of toric or…
We study the subvariety of singular sections, the discriminant, of a base point free linear system $|L|$ on a smooth toric variety $X$. On one hand we describe pairs $(X,L)$ for which the discriminant is of low dimension. Precisely, we…
Using the natural duality between linear functionals on tensor products of C*-algebras with the trace class operators on a Hilbert space H and linear maps of the C*-algebra into B(H), we give two characterizations of separability, one…
In the present article, we investigate the topology of real toric varieties, especially those whose torus is not split over the field of real numbers. We describe some canonical fibrations associated to their real loci. Then, we establish…
Let $M$ be a complex manifold. We prove that a compact submanifold $S\subset M$ with splitting tangent sequence (called a splitting submanifold) is rational homogeneous when $M$ is in a large class of rational homogeneous spaces of Picard…
It is shown that separation conditions (separation curves) are fundamental objects of separability theory. They are used for the classification of certain clases of separable systems, for the proof of bi-Hamiltonian property and finally…
A separating algebra is, roughly speaking, a subalgebra of the ring of invariants whose elements distinguish between any two orbits that can be distinguished using invariants. In this paper, we introduce a geometric notion of separating…
The main result of this paper is that every (separated) toric variety which has a semigroup structure compatible with multiplication on the underlying torus is necessarily affine. In the course of proving this statement, we also give a…
In this paper, we study the persistent homology of the offset filtration of algebraic varieties. We prove the algebraicity of two quantities central to the computation of persistent homology. Moreover, we connect persistent homology and…
Two subsets $A, B$ of the plane are betweenness isomorphic if there is a bijection $f\colon A\to B$ such that, for every $x,y,z\in A$, the point $f(z)$ lies on the line segment connecting $f(x)$ and $f(y)$ if and only if $z$ lies on the…
The properties of the spaces of Sugeno integrable functions are quite different from those of the ordinary spaces of Lebesgue integrable functions. The purpose of the paper is to further advance our study of the Sugeno-Lorentz spaces, in…
The new type of solutions of the London equation for type-II superconductors is obtained to describe the ring-shaped (toroidal) Abrikosov vortices. The specific feature of these solutions is the self-consistent localization of both the…
We show that in a finite tensor category, the tensor product property holds for support varieties if and only if it holds between indecomposable periodic objects. We apply this to certain Hopf algebras in the form of skew group algebras. In…
We consider the covering map $\pi:\mathbb{C}^n\to \mathbb{T}$ of a compact complex torus. Given an algebraic variety $X\subseteq \mathbb{C}^n$ we describe the topological closure of $\pi(X)$ in $\mathbb T$. We obtain a similar description…
This thesis is devoted to the study of geometric properties of affine algebraic varieties endowed with an action of an algebraic torus. It comes from three preprints which correspond to the indicated points (1), (2), (3). Let $X$ be an…
The subject of this paper is the problem of arrangement of real algebraic curves on real algebraic surfaces. In this paper we extend Rokhlin, Kharlamov-Gudkov-Krakhnov and Kharlamov-Marin congruences for curves on surfaces and give some…
Let $V$ be a complex finite dimensional super vector space with an action of a connected semisimple group $G$. We classify those pairs $(G,V)$ for which all homogeneous components of the super symmetric algebra of $V$ decompose…
We study homotopy rational points of Brauer-Severi varieties over fields of characteristic zero. We are particularly interested if a Brauer-Severi variety admitting a homotopy rational point splits. The analogue statement turns out to be…
Starting from an abstract elementary class with no maximal models, Shelah and Villaveces have shown (assuming instances of diamond) that categoricity implies a superstability-like property for a certain independence relation called…
This paper deals with properties of filtrations on vector spaces indexed by partially ordered finitely generated abelian groups, which we call multifiltrations. We discuss the usual properties of filtrations, like exhaustivity and…
The paper presents some weak compactness criterion for a subset $M$ of the set $\mathfrak{RM}_b(T,\mathcal{G})$ of all positive bounded Radon measures on a Hausdorff topological space $(T,\mathcal{G})$ similar to the Prokhorov criterion for…