相关论文: On planar webs with infinitesimal automorphisms

In this note we prove that every finite collection of connected algebraic subgroups of the group of triangular automorphisms of the affine space generates a connected solvable algebraic subgroup.

We study relations between cluster algebra invariants and link invariants. First, we show that several constructions of positroid links (permutation links, Richardson links, grid diagram links, plabic graph links) give rise to isotopic…

We extend the differential form representation of N = (n,n) supersymmetric quantum mechanics to the superconformal case. We identify the superalgebras occurring for n = 1,2,4, give necessary and sufficient conditions for their existence,…

We construct a new class of affine complements ${\mathbb P}^M\setminus S$ with the trivial group of automorphisms, where $S\subset {\mathbb P}^M$ is a rational hypersurface, $M$ is odd and $M\geqslant 5$.

Given a variety of universal algebras. A method is suggested for describing automorphisms of a category of free algebras of this variety. Applying this general method all automorphisms of such categories are found in two cases: 1) for the…

In this paper we introduce a family of planar, modular and self-similar graphs which have small-world and scale-free properties. The main parameters of this family are comparable to those of networks associated to complex systems, and…

We classify $N{=}1$ $d=4$ kinematical and aristotelian Lie superalgebras with spatial isotropy, but not necessarily parity nor time-reversal invariance. Employing a quaternionic formalism which makes rotational covariance manifest and…

We show that if a field k contains sufficiently many elements(for instance, if k is infinite), and K is an algebraically closed field containing k, then every linear algebraic k-group over K is k-isomorphic to Aut(A\otimes_kK), where A is a…

We examine properties of generic automorphisms of the random poset, with the goal of explicitly characterizing them. We associate to each automorphism an auxiliary first-order structure, consisting of the random poset equipped with an…

We present a survey of the calibrated geometries arising in the study of the local singularity structure of supersymmetric fivebranes in M-theory. We pay particular attention to the geometries of 4-planes in eight dimensions, for which we…

We construct non-isogenous simple ordinary abelian varieties over an algebraic closure of a finite field with isomorphic endomorphism algebras.

We construct examples of algebraic surfaces with interesting fundamental groups.

We study the maximum number of straight-line segments connecting $n$ points in convex position in the plane, so that each segment intersects at most $k$ others. This question can also be framed as the maximum number of edges of an outer…

This work presents the conjugacy classes of finite abelian subgroups of the Cremona group of the plane. Using a well-known theory, this problem amounts to the study of automorphism groups of some Del Pezzo surfaces and conic bundles. We…

We construct a new family of infinite-dimensional quasi-graded Lie algebras on hyperelliptic curves. We show that constructed algebras possess infinite number of invariant functions and admit a decomposition into the direct sum of two…

Let $A$ be an abelian variety over a finite field $k$. The $k$-isogeny class of $A$ is uniquely determined by the Weil polynomial $f_A$. We assume that $f_A$ is separable. For a given prime number $\ell\neq\mathrm{char}\, k$ we give a…

We study the homeomorphism types of certain covers of (always orientable) surfaces, usually of infinite-type. We show that every surface with non-abelian fundamental group is covered by every noncompact surface, we identify the universal…

Let $A$ be an abelian surface over a finite field $k$. The $k$-isogeny class of $A$ is uniquely determined by a Weil polynomial $f_A$ of degree 4. We give a classification of the groups of $k$-rational points on varieties from this class in…

We call every complex connected (1,1)-dimensional supermanifold a super Riemann surface and construct versal super families of compact ones, where the base spaces are allowed to be certain ringed spaces including all complex supermanifolds.…

We construct new families of discrete vector orthogonal polynomials that have the property to be eigenfunctions of some difference operator. They are extensions of Charlier, Meixner and Kravchuk polynomial systems. The ideas behind our…