Related papers: Complete intersections in certain affine and proje…

In recent work of T. Cassidy and the author, a notion of complete intersection was defined for (non-commutative) regular skew polynomial rings, defining it using both algebraic and geometric tools, where the commutative definition is a…

Let k be an algebraically closed field of positive characteristic. The goal of this paper is to characterize the proper smooth curves X/k of positive genus g equipped with a k-rational point P such that X\P can be realized as an etale cover…

This paper is a continuation of a previous work by the author and G. Puninski where iterated intersections of powers of ideals were studied in rings of iterated differential polynomials. We present a method which can be used to show that…

We prove that entire conformal curves $\mathbb{R}^n \rightarrow \mathbb{R}^m$ fall into two classes: either the curve is affine or the average energy in a ball is strictly increasing for large radii and diverges to infinity. This rigidity…

Amoebas are projections of complex algebraic varieties in the algebraic torus under a Log-absolute value map, which have connections to various mathematical subjects. While amoebas of hypersurfaces have been intensively studied in recent…

We present a class of toric varieties $V$ which, over any algebraically closed field of characteristic zero, are defined by codim $V$+1 binomial equations.

Let $I$ be ideal of an $n$-dimensional local Gorenstein ring $R$. In this paper we will describe several necessary and sufficient conditions such that the ideal $I$ becomes cohomologically complete intersections. In fact, as a technical…

Let R be monomial sub-algebra of $k[x_1,...,x_N]$ generated by square free monomials of degree two. This paper addresses the following question: when is R a complete intersection? For such a k-algebra we can associate a graph G whose…

In this paper, we consider point sets of finite Desarguesian planes whose multisets of intersection numbers with lines is the same for all but one exceptional parallel class of lines. We call such sets regular of affine type. When the lines…

In this paper our aim is twofold. First, we introduce the notion of star gluing of numerical semigroups and show that arithmetically Cohen-Macaulay and Gorenstein properties of the projective closure are preserved under this gluing…

Given an affine algebraic variety V and a quantization A of its coordinate ring, it is conjectured that the primitive ideal space of A can be expressed as a topological quotient of V. Evidence in favor of this conjecture is discussed, and…

We prove that the initial ideal of the defining ideal of a monomial curve that corresponds to an almost arithmetic sequence of positive integers is Ratliff-Rush closed.

A complete intersection $f_1=\cdots=f_k=0$ is sch\"on, if $f_1=\cdots=f_j=0$ defines a sch\"on subvariety of an algebraic torus for every $j\leqslant k$. This class includes nondegenerate complete intersections, critical loci of their…

In this paper we give conditions on a homogeneous polynomial for which the associated graded Artin algebra is a complete intersection.

Let $A$ denote an affine algebra over an algebraically closed field $k$, with $\dim A=d\geq 3$. In the light of availability of cancellation theorems for stably free modules $P$ with $rank(P)=d-1$ (corank one), we try to implement the…

Let $K$ be an arbitrary field. Let $\a = (a_1< ... <a_n)$ be a sequence of positive integers. Let $C(\a)$ be the affine monomial curve in ${\mathbb A}^n$ parametrized by $t\to (t^{a_1}, ..., t^{a_n})$. Let $I(\a)$ be the defining ideal of…

The goal of this short note is to prove that when $A$ is a closed *-subalgebra of a C*-algebra $B$ satisfying the ideal intersection property plus a mild axiom (INV), then the map $J\mapsto J\cap A$ establishes an isomorphism from the…

Let G be a finite simple graph. In this paper we will show that the binomial edge ideal of G, JG is toric if and only if each connected component of G is complete and in this case it is the sum of toric ideal associated to bipartite…

The aim of this note is to exploit a new relationship between additive combinatorics and the geometry of monomial projective curves. We associate to a finite set of non-negative integers $A=\{a_1,\cdots, a_n\}$ a monomial projective curve…

We prove that a complete intersection of $c$ very general hypersurfaces of degree at least two in $N$-dimensional complex projective space is not ruled (and therefore not rational) provided that the sum of the degrees of the hypersurfaces…