相关论文: The Limiting Polytope of the Generic Initial Syste…

We consider complete intersection ideals in a polynomial ring over a field of characteristic zero that are stable under the action of the symmetric group permuting the variables. We determine the possible representation types for these…

We prove that the $d$-component of the generic initial ideal, with respect to the reverse lexicographic order, of an ideal generated by a regular sequence of homogeneous polynomials of degree $d$ is revlex in a particular, but important,…

We compute the reverse lexicographic generic initial ideals of the powers of a 2-complete intersection ideal I. In particular, we give six algorithms to compute these generic initial ideals, the choice of which depends on the power and on…

Consider the ideal I in K[x,y,z] corresponding to six points of P2. We study the limiting behaviour of the symbolic generic initial system, of I obtained by taking the reverse lexicographic generic initial ideals of the symbolic powers of…

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…

The arithmetic rank of an ideal in a polynomial ring over an algebraically closed field is the smallest number of equations needed to define its vanishing locus set-theoretically. We determine the arithmetic rank of the generic $m$-residual…

Consider the ideal I corresponding to r points in P^2. We study the symbolic generic initial system of I, formed by taking the generic initial ideals of the symbolic powers of I, and its asymptotic behaviour. In particular, we describe the…

Let $R = K[x_1, x_2, x_3, x_4]$ be the polynomial ring over a field of characteristic zero. For the ideal $(x_1^a, x_2^b, x_3^c, x_4^d) \subset R$, where at least one of $a$, $b$, $c$ and $d$ is equal to two, we prove that its generic…

Given a graded ideal $I$ in a polynomial ring over a field $K$ it is well known, that the number of distinct generic initial ideals of $I$ is finite. While it is known that for a given $d\in\N$ there is a global upper bound for the number…

We study almost complete intersection ideals in a polynomial ring, generated by powers of all the variables together with a power of their sum. Our main result is an explicit description of the reduced Gr\"obner bases for these ideals under…

For the family of graded lattice ideals of dimension 1, we establish a complete intersection criterion in algebraic and geometric terms. In positive characteristic, it is shown that all ideals of this family are binomial set theoretic…

It has been shown that the edge structure of the characteristic imset polytope is closely connected to the question of causal discovery. The diameter of a polytope is an indicator of how connected the polytope is and moreover gives us 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 classify all unmixed monomial ideals I of codimension 2 which are generically a complete intersection and which have the property that the symbolic power algebra A(I) is standard graded. We give a lower bound for the highest degree of a…

A restricted $d$th power of an ideal $I$ is obtained by restricting the exponent vectors allowed to appear on the "natural" generating set of $I^d$, for some integer $d$. In this paper, we study homological properties of restricted powers…

In this article we introduce and study the intersection graph of graded ideals of graded rings. The intersection graph of $G-$graded ideals of a graded ring $(R,G)$ is a simple graph, denoted by $Gr_G(R)$, whose vertices are the nontrivial…

Consider an ideal I in K[x,y,z] corresponding to a point configuration in P2 where all but one of the points lies on a single line. In this paper we study the symbolic generic initial system obtained by taking the reverse lexicographic…

A complete intersection of n polynomials in n indeterminates has only a finite number of zeros. In this paper we address the following question: how do the zeros change when the coefficients of the polynomials are perturbed? In the first…

Let I and J be homogeneous ideals in a standard graded polynomial ring. We study upper bounds of the Hilbert function of the intersection of I and g(J), where g is a general change of coordinates. Our main result gives a generalization of…

Given a 0-dimensional affine K-algebra R=K[x_1,...,x_n]/I, where I is an ideal in a polynomial ring K[x_1,...,x_n] over a field K, or, equivalently, given a 0-dimensional affine scheme, we construct effective algorithms for checking whether…