Related papers: The Symbolic Generic Initial System of Points on a…
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…
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…
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…
Consider a complete intersection I of type (d_1,..., d_r) in a polynomial ring over a field of characteristic 0. We study the graded system of ideals {gin(I^n)}_n obtained by taking the reverse lexicographic generic initial ideals of the…
We study initial degrees of symbolic powers of ideals of arbitrary finite sets of points in the projective plane over an algebraically closed field of characteristic zero. We show, how bounds on the growth of these degrees determine the…
The purpose of this note is to describe limiting shapes (as introduced by Mayes) of symbolic generic initial systems of star configurations in projective spaces over a field of characteristic 0.
Given a symbolic power of a homogeneous ideal in a polynomial ring, we study the problem of determining which powers of the ideal contain it. For ideals defining 0-dimensional subschemes of projective space, as an immediate corollary of our…
An ideal I of a commutative ring R is said to be irreducible if it cannot be written as the intersection of two larger ideals. A proper ideal I of a ring R is said to be strongly irreducible if for each ideals J, K of R, J\cap K\subseteq I…
Given distinct points $p_1,\cdots,p_r$ of the projective plane $P^2$ and a positive integer $m$, the homogeneous ideal defining the fat point subscheme $Z=m(p_1+\cdots+p_r)$ is the symbolic power $I^{(m)}$ of the homogeneous ideal $I$…
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…
Given an ideal $I$ in a Noetherian ring, one can ask the containment question: for which $m$ and $r$ is the symbolic power $I^{(m)}$ contained in the ordinary power $I^r$? C. Bocci and B. Harbourne study the containment question in a…
We study the irreducible complex representations of general linear groups over principal ideal local rings of length two with a fixed finite residue field. We construct a canonical correspondence between the irreducible representations of…
We define basic notions in the category of conic representations of a topological group and prove elementary facts about them. We show that a conic representation determines an ordinary dynamical system of the group together with a…
One deals with catalectic codimension two perfect ideals and certain degenerations thereof, with a view towards the nature of their symbolic powers. In the spirit of [10] one considers linearly presented such ideals, only now in the…
We consider the multigraded Hilbert scheme corresponding to the Hilbert function of a finite number of points in general position in a smooth projective complex toric variety. We develop several criteria for a point of that parameter space…
We show that there exist $\mathbb{Z}^{2}$ symbolic systems that are strongly irreducible and have no (fully) periodic points
Let I be the defining ideal of a smooth irreducible complete intersection space curve C with defining equations of degrees a and b. We use the partial elimination ideals introduced by Mark Green to show that the lexicographic generic…
Let P(x,y) be a rational polynomial and k in Q be a generic value. If the curve (P(x,y)=k) is irreducible and admits an infinite number of points whose coordinates are integers then there exist algebraic automorphisms that send P(x,y) to…
Several known constructions relate initial degenerations of projective toric varieties and Grassmannians to regular subdivisions of appropriate point configurations. We define a general framework which allows for partial generalizations of…
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…