相关论文: Upper Bounds for Betti Numbers of Multigraded Modu…

The extremal values of multivariate trigonometric polynomials are of interest in fields ranging from control theory to filter design, but finding the extremal values of such a polynomial is generally NP-Hard. In this paper, we develop…

In the present paper, we give an upper bound for the generic degree of the generalized Verschiebung between the moduli spaces of rank two stable bundles with trivial determinant.

We determined the first two Betti numbers of the moduli of rank two stable sheaves on an arbitrary algebraic surface

Let $K$ be a field, $V$ a $K$-vector space with basis $e_1,\ldots,e_n$, and $E$ the exterior algebra of $V$. To a given monomial ideal $I\subsetneq E$ we associate a special monomial ideal $J$ with generators in the same degrees as those of…

We provide explicit bounds on the difference of heights of isogenous Drinfeld modules. We derive a finiteness result in isogeny classes. In the rank 2 case, we also obtain an explicit upper bound on the size of the coefficients of modular…

Let K be a field and let S = K[x_1, ..., x_n] be a polynomial ring. Consider a homogenous ideal I in S. Let t_i denote reg(Tor_i (S/I, K)), the maximal degree of an ith syzygy of S/I. We prove bounds on the numbers t_i for i > n/2 purely in…

We prove an upper bound on the rank of the abelianised revised fundamental group (called "revised first Betti number") of a compact $RCD^{*}(K,N)$ space, in the same spirit of the celebrated Gromov-Gallot upper bound on the first Betti…

In this paper, we study the structure of set-multilinear arithmetic circuits and set-multilinear branching programs with the aim of showing lower bound results. We define some natural restrictions of these models for which we are able to…

In this paper we propose a general method for computing a minimal free right resolution of a finitely presented graded right module over a finitely presented graded noncommutative algebra. In particular, if such module is the base field of…

We obtain general criteria for giving a lower bound on the degree of numbers of the form $\prod_{n=1}^\infty \left(1+\frac{b_n}{\alpha_n}\right)$ or of the form $\prod_{m=1}^\infty \left(1+ \sum_{n=1}^\infty…

It is known that sometimes a Belyi pair is not defined over its field of moduli. Instead, it is defined over a finite degree extension of its field of moduli, called a field of definition. We show that given a number $m$ there exists a…

Let $\Lambda$ be a basic finite dimensional algebra over an algebraically closed field, presented as a path algebra modulo relations; further, assume that $\Lambda$ is graded by lengths of paths. The paper addresses the classifiability, via…

We characterize in certain basic cases when a module over a ring is either {\it hereditarily Bassian} or {\it super Bassian} in the sense that either each its proper submodule is Bassian or, respectively, each its proper epimorphic image is…

We present the shift-dimension of multipersistence modules and investigate its algebraic properties. This gives rise to a new invariant of multigraded modules over the multivariate polynomial ring arising from the hierarchical stabilization…

Let $k$ be a field and $R=k[x_1,\ldots,x_n]/I=S/I$ a graded ring. Then $R$ has a $t$-linear resolution if $I$ is generated by homogeneous elements of degree $t$, and all higher syzygies are linear. Thus $R$ has a $t$-linear resolution if…

Upper bounds on the maximum number of codewords in a binary code of a given length and minimum Hamming distance are considered. New bounds are derived by a combination of linear programming and counting arguments. Some of these bounds…

We express Wronskian Hermite polynomials in the Hermite basis and obtain an explicit formula for the coefficients. From this we deduce an upper bound for the modulus of the roots in the case of partitions of length 2. We also derive a…

Let $S = K[x_1, ..., x_n]$ denote the polynomial ring in $n$ variables over a field $K$ with each $\deg x_i = 1$. Let $\Delta$ be a simplicial complex on $[n] = \{1, ..., n \}$ and $I_\Delta \subset S$ its Stanley--Reisner ideal. We write…

For any elements b,c of a number field K, let G(b,c) denote the backwards orbit of b under the map f_c: C-->C given by f_c(x)=x^2+c. We prove an upper bound on the number of elements of G(b,c) whose degree over K is at most some constant B.…

We prove a lower bound on the canonical height associated to polynomials over number fields evaluated at points with infinite forward orbit. The lower bound depends only on the degree of the polynomial, the degree of the number field, and…