Related papers: Dimensions of monomial varieties
We obtain new bounds of multivariate exponential sums with monomials, when the variables run over rather short intervals. Furthermore, we use the same method to derive estimates on similar sums with multiplicative characters to which…
We prove a sharp degree bound for polynomials constant on a hyperplane with a fixed number of distinct monomials for dimensions 2 and 3. We study the connection with monomial CR maps of hyperquadrics and prove similar bounds in this setup…
Assume that $V$ is a braided vector space with diagonal type. It is shown that a monomial belongs to Nichols braided Lie algebra $\mathfrak L(V)$ if and only if this monomial is connected. A basis of Nichols braided Lie algebra and…
We study the arithmetical ranks and the cohomological dimensions of an infinite class of Cohen-Macaulay varieties of minimal degree. Among these we find, on the one hand, infinitely many set-theoretic complete intersections, on the other…
We construct monomial ideals with the property that their depth function has any given number of strict local maxima.
Given a complex algebraic variety X, we define a natural number called the motivic dimension which measures the amount of transcendental (co)homology of X. It is zero precisely when all the (co)homolgy is spanned by algebraic cycles. Most…
Second-order automorphic forms are similar to the usual automorphic forms but have a weaker automorphy condition. We answer a question of Zagier and find the dimensions of spaces of holomorphic, even weight, second-order forms. We also…
We consider some special type extensions of an arbitrary Lie algebra, which we call universal extensions. We show that these extensions are in one-to-one correspondence with finite dimensional associative commutative algebras. We also…
Tropical mathematics redefines the rules of arithmetic by replacing addition with taking a maximum, and by replacing multiplication with addition. After briefly discussing a tropical version of linear algebra, we study polynomials build…
Permutation polynomials over finite fields play important roles in finite fields theory. They also have wide applications in many areas of science and engineering such as coding theory, cryptography, combinatorial design, communication…
In this article, we give a complete description of the characteristic polynomials of supersingular abelian varieties over finite fields. We list them for the dimensions upto 7.
Both a general and a diagonal u-invariant for forms of higher degree are defined, generalizing the u-invariant of quadratic forms. Both old and new results on these invariants are collected.
Algebraic and combinatorial properties of a monomial ideal and its radical are compared.
New finite-dimensional representations of specific polynomial deformations of sl(2,R) are constructed. The corresponding generators can be, in particular, realized through linear differential operators preserving a finite-dimensional…
We consider the functions that bound the dimensions of finite-dimensional associative or Lie algebras in terms of the dimensions of their commutative subalgebras. It is proved that these functions have quadratic growth. As a result, we also…
The purpose of this paper is to describe the images of multilinear polynomials of arbitrary degree on the strictly upper triangular matrix algebra.
Positively graded algebras are fairly natural objects which are arduous to be studied. In this article we query quotients of non-standard graded polynomial rings with combinatorial and commutative algebra methods.
For each 3-dimensional non-Lie Leibniz algebra over the complex numbers, we describe the algebra of polynomial invariants and determine its group of automorphisms. As a consequence, we establish that any two non-nilpotent 3-dimensional…
We present two approaches, one homological and the other simplicial, for the investigation of dimension quotients of groups. The theory is illustrated, in particular, with a conceptual discussion of the fourth and fifth dimension quotients.
We give criteria for Morin singularities into higher dimensions. As an application, we study the number of A-isotopy classes of Morin singularities.