Related papers: The orbit intersection problem for linear spaces a…

We prove that any proper Fourier-Mukai partner of an abelian variety is again an abelian variety, by analyzing the Matsui spectrum of the derived category. This result was previously obtained by Huybrechts and Nieper-Wisskirchen in the case…

We consider two algorithmic problems concerning sub-semigroups of Heisenberg groups and, more generally, two-step nilpotent groups. The first problem is Intersection Emptiness, which asks whether a finite number of given finitely generated…

We consider a dynamics of a generic birational plane map \Phi_n: CP^2 \to CP^2, CP^2 -image of the birational mapping (inverse map is also rational)F_n : C^2 \to C^2 and its such important characteristic as the Arnold complexity C_A(k),…

In this paper, we study local solutions F=(F1,..,Fn) of a general functional equation of the form F1(U1(x,y))+....+Fn(Un(x,y))=0. A such equation will be called an ``abelian functional equation'' (Afe). We will restrict ourselves to the…

We give a combinatorial algorithm for computing Zelevinsky's involution of the set of isomorphism classes of irreducible representations of the affine Hecke algebra $\H_m(t)$ when $t$ is a primitive $n$th root of 1. We show that the same…

Let $K$ be a totally real number field of degree $n \geq 2$. The inverse different of $K$ gives rise to a lattice in $\mathbb{R}^n$. We prove that the space of Schwartz Fourier eigenfunctions on $\mathbb{R}^n$ which vanish on the…

In this paper we study combinatorial aspects of permutations of $\{1,\ldots,n\}$ and related topics. In particular, we prove that there is a unique permutation $\pi$ of $\{1,\ldots,n\}$ such that all the numbers $k+\pi(k)$ ($k=1,\ldots,n$)…

We present a new look at description of real finite-dimensional Lie algebras. The basic element turns out to be a pair $(F,v)$ consisting of a linear mapping $F\in End(V)$ and its eigenvector $v$. This pair allows to build a Lie bracket on…

Ritt studied the functional decomposition of a univariate complex polynomial f into prime (indecomposable) polynomials, f = u_1 o u_2 o ... o u_r. His main achievement was a procedure for obtaining any decomposition of f from any other by…

We study sets of nontypical points under the map $f_\beta \mapsto \beta x $ mod 1, for non-integer $\beta$ and extend our results from [F\"arm, Persson, Schmeling, 2010] in several directions. In particular we prove that sets of points…

Given any polynomial system with fixed monomial term structure, we give explicit formulae for the generic number of roots with specified coordinate vanishing restrictions. For the case of affine space minus an arbitrary union of coordinate…

Let X be a very general complete intersection in complex projective space and we denote by $F_r(X)$ the variety of r-planes in X, for $r\geq 1$. We show that the Picard number of $F_r(X)$ is 1, as soon as $\dim F_r(X)\geq 2$, except when X…

Let $p$ be a prime, $m$ be a positive integer ( $m \geq 1$, and $m \geq 2$ if $p=2$), and $\chi_n$ be a multiplicative complex character on $\mathbb F^*_{p^m}$ with order $n| (p^m-1)$. We show that a partition $\mathcal A_1 \cup \mathcal…

Considering a finite intersection of balls and a finite union of other balls in an Euclidean space, we propose an exact method to test whether the intersection is covered by the union. We reformulate this problem into quadratic programming…

Given positive integers $e_1,e_2$, let $X_i$ denote the set of $e_i$-dimensional subspaces of a fixed finite vector space $V=(\mathbb{F}_q)^{e_1+e_2}$. Let $Y_i$ be a non-empty subset of $X_i$ and let $\alpha_i=|Y_i|/|X_i|$. We give a…

We consider commutativity equations $F_i F_j =F_j F_i$ for a function $F(x^1, \dots, x^N),$ where $F_i$ is a matrix of the third order derivatives $F_{ikl}$. We show that under certain non-degeneracy conditions a solution $F$ satisfies the…

We prove that for a bijective, unital, linear map between absolute order unit spaces is an isometry if, and only if, it is absolute value preserving. We deduce that, on (unital) $JB$-algebras, such maps are precisely Jordan isomorphisms.…

Consider the algebraic dynamics on a torus T=G_m^n given by a matrix M in GL_n(Z). Assume that the characteristic polynomial of M is prime to all polynomials X^m-1. We show that any finite equivariant map from another algebraic dynamics…

Suppose $F$ is an infinite field and let $f \in F\{X_1, \dots,X_m\}$ be a noncommutative polynomial. Partially answering a query of Makar-Limanov, we show that there are numbers $d$ and $m'$ such that, if $F$ is closed under taking $d$th…

Let $F_1,\ldots,F_R$ be homogeneous polynomials of degree $d\ge 2$ with integer coefficients in $n$ variables, and let $\mathbf{F}=(F_1,\ldots,F_R)$. Suppose that $F_1,\ldots,F_R$ is a non-singular system and $n\ge 4^{d+2}d^2R^5$. We prove…