Related papers: Complete intersections in certain affine and proje…

Let $(A,\mathfrak{m})$ be an abstract complete intersection and let $P$ be a prime ideal of $A$. In [1] Avramov proved that $A_P$ is an abstract complete intersection. In this paper we give an elementary proof of this result.

Let $G$ be a group. The intersection graph of subgroups of $G$, denoted by $\mathscr{I}(G)$, is a graph with all the proper subgroups of $G$ as its vertices and two distinct vertices in $\mathscr{I}(G)$ are adjacent if and only if the…

Let $\Lambda$ be a numerical semigroup, $\mathcal{C}\subseteq \mathbb{A}^n$ the monomial curve singularity associated to $\Lambda$, and $\mathcal{T}$ its tangent cone. In this paper we provide a sharp upper bound for the least positive…

In this paper we extend a result of Cowsik on set-theoretic complete intersection and a result Huneke, Morales and Goto and Nishida about Noetherian symbolic Rees algebras of ideals. As applications, we show that the symbolic Rees algebras…

We develop an approach to study the irreducibility of generic complete intersections in the algebraic torus defined by equations with fixed monomials and fixed linear relations on coefficients. Using our approach we generalize the…

A graph-theoretic method, simpler than existing ones, is used to characterize the minimal set of monomial generators for the integral closure of any algebra of polynomials generated by quadratic monomials. The toric ideal of relations…

Let $k$ be any field. Let $R=k[[X_1,\ldots,X_d]]$ and $\frak p$ a $1$-dimensional prime ideal. In this note we present $d-1$ elements such as $f_1,\ldots,f_{d-1}$ in $\frak p$ such that $\mathfrak{p}=\text{rad}(f_1,\ldots,f_{d-1})$.

In this article we give explicit descriptions of the multiplicities of some classes of monomial ideals. For instance, we give a formula for the multiplicities of all codimension 1 monomial ideals, and another formula for the multiplicities…

We describe a class of affine toric varieties $V$ that are set-theoretically minimally defined by codim $V+1$ binomial equations over fields of any characteristic.

This article will appear in the proceedings of the AMS Summer Institute in Algebraic Geometry at Santa Cruz, July 1995. The topic is toric ideals, by which I mean the defining ideals of subvarieties of affine or projective space which are…

Let $K$ be an infinite field and let $m_1,\ldots,m_n$ be a generalized arithmetic sequence of positive integers, i.e., there exist $h, d, m_1 \in\mathbb{Z}^+$ such that $m_i = h m_1 + (i-1)d$ for all $i \in \{2,\ldots,n\}$. We consider the…

Global F-theory compactifications whose fibers are realized as complete intersections form a richer set of models than just hypersurfaces. The detailed study of the physics associated with such geometries depends crucially on being able to…

This paper studies algebraic residual intersections in rings with Serre's condition \( S_{s} \). It demonstrates that residual intersections admit free approaches i.e. perfect subideal with the same radical. This fact leads to determining a…

In this article we prove that every toric ideal associated with a gap-free graph $G$ has a squarefree lexicographic initial ideal. Moreover, in the particular case when the complementary graph of $G$ is chordal (i.e. when the edge ideal of…

The aim of this paper is to provide an explicit basis of the miniversal deformation of a monomial curve defined by a free semigroup -- these curves make up a notable family of complete intersection monomial curves. First, we dispense a…

In this paper we prove conditions for transversal intersection of monomial ideals and derive a simplicial characterization of this phenomenon.

In this paper, we provide a combinatorial characterization of those collections of cells whose inner $2$-minor ideals are complete intersections. More precisely, given a collection of cells $\mathcal C$ and its associated inner $2$-minor…

One of the goals of this paper is to prove that the index of intersection of two complex curves in a two-dimensional complex manifold tangent to each other at a common boundary point is positive. This is achieved via the construction of a…

The properties of the intersection algebra of two principal monomial ideals in a polynomial ring are investigated in detail. Results are obtained regarding the Hilbert series and the canonical ideal of the intersection algebra using methods…

We compute the expectation of the number of linear spaces on a random complete intersection in $p$-adic projective space. Here "random" means that the coefficients of the polynomials defining the complete intersections are sampled uniformly…