Star configurations in Pn
TLDR
In this paper, the authors studied algebraic properties of the ideals defining star configurations, including partial results about Hilbert functions, generators and minimal free resolutions of ideals and their symbolic powers.About:
This article is published in Journal of Algebra.The article was published on 2013-02-15 and is currently open access. It has received 111 citations till now. The article focuses on the topics: Algebraic variety & Projective space.read more
Citations
More filters
Journal ArticleDOI
Asymptotic resurgences for ideals of positive dimensional subschemes of projective space
TL;DR: In this paper, Bocci-Harbourne and Harbourne defined a resurgence quantity for homogeneous ideals in polynomial rings, with a focus on zero-dimensional subschemes of projective space.
Journal ArticleDOI
Linear subspaces, symbolic powers and Nagata type conjectures
TL;DR: In this paper, the least degree of a homogeneous form vanishing to order at least m on a union of disjoint r-dimensional planes in P n for n ⩾ 2 r + 1.
Journal ArticleDOI
Line arrangements and configurations of points with an unusual geometric property
TL;DR: In this article, a generalization of the SHGH conjecture is proposed, where rational curves play a similar role in a special case of a generalized problem, which asks how many conditions are imposed by a general union of fat points on linear subsystems defined by imposed base points.
Journal ArticleDOI
On the containment problem
Tomasz Szemberg,Justyna Szpond +1 more
TL;DR: In this paper, the authors provide an overview of the containment problem for symbolic and ordinary powers of homogeneous ideals, related conjectures and examples, focusing here on ideals with zero dimensional support.
Journal ArticleDOI
Hadamard products of linear spaces
TL;DR: In this paper, it was shown that any Hadamard power of a line is a linear space and that any star configuration can be constructed from products of collinear points.
References
More filters
Book
Introduction to Commutative Algebra
TL;DR: It is shown here how the Noetherian Rings and Dedekind Domains can be transformed into rings and Modules of Fractions using the following structures:
Commutative Algebra I
TL;DR: A compilation of two sets of notes at the University of Kansas was published in the Spring of 2002 by?? and the other in the spring of 2007 by Branden Stone.
Journal ArticleDOI
Cohen-Macaulay Rings, Invariant Theory, and the Generic Perfection of Determinantal Loci
Melvin Hochster,J. A. Eagon +1 more
TL;DR: In this paper, it was shown that if I can be generated by r elements, then the rank or altitude of I (the greatest rank of any minimal prime of I) is at most r.
Book
Introduction to Liaison Theory and Deficiency Modules
TL;DR: In this paper, the Hartshorne-Schenzel theorem is used to define a liaison class and the structure of an even liaison class geometric invariants of a relationship class.