Line arrangements and configurations of points with an unexpected geometric property
D Cook, B Harbourne, J Migliore, U Nagel - Compositio Mathematica, 2018 - cambridge.org
We propose here a generalization of the problem addressed by the SHGH conjecture. The
SHGH conjecture posits a solution to the question of how many conditions a general union …
SHGH conjecture posits a solution to the question of how many conditions a general union …
Asymptotic resurgence via integral closures
M DiPasquale, C Francisco, J Mermin… - Transactions of the …, 2019 - ams.org
Given an ideal in a polynomial ring, we show that the asymptotic resurgence studied by
Guardo, Harbourne, and Van Tuyl can be computed using integral closures. As a …
Guardo, Harbourne, and Van Tuyl can be computed using integral closures. As a …
Chudnovsky's conjecture and the stable Harbourne–Huneke containment
We investigate containment statements between symbolic and ordinary powers and bounds
on the Waldschmidt constant of defining ideals of points in projective spaces. We establish …
on the Waldschmidt constant of defining ideals of points in projective spaces. We establish …
Expected resurgences and symbolic powers of ideals
We give explicit criteria that imply the resurgence of a self‐radical ideal in a regular ring is
strictly smaller than its codimension, which in turn implies that the stable version of …
strictly smaller than its codimension, which in turn implies that the stable version of …
[HTML][HTML] A stable version of Harbourne's Conjecture and the containment problem for space monomial curves
E Grifo - Journal of Pure and Applied Algebra, 2020 - Elsevier
The symbolic powers I (n) of a radical ideal I in a polynomial ring consist of the functions that
vanish up to order n in the variety defined by I. These do not necessarily coincide with the …
vanish up to order n in the variety defined by I. These do not necessarily coincide with the …
Singular loci of reflection arrangements and the containment problem
B Drabkin, A Seceleanu - Mathematische Zeitschrift, 2021 - Springer
This paper provides insights into the role of symmetry in studying polynomial functions
vanishing to high order on an algebraic variety. The varieties we study are singular loci of …
vanishing to high order on an algebraic variety. The varieties we study are singular loci of …
On resurgence via asymptotic resurgence
M DiPasquale, B Drabkin - Journal of Algebra, 2021 - Elsevier
The resurgence and asymptotic resurgence of an ideal in a polynomial ring are two statistics
which measure the relationship between its regular and symbolic powers. We address two …
which measure the relationship between its regular and symbolic powers. We address two …
Symbolic rees algebras
E Grifo, A Seceleanu - … Algebra: Expository Papers Dedicated to David …, 2021 - Springer
We survey old and new approaches to the study of symbolic powers of ideals. Our focus is
on the symbolic Rees algebra of an ideal, viewed both as a tool to investigate its symbolic …
on the symbolic Rees algebra of an ideal, viewed both as a tool to investigate its symbolic …
Real and complex supersolvable line arrangements in the projective plane
K Hanumanthu, B Harbourne - Journal of Algebraic Combinatorics, 2021 - Springer
If we regard a set of s lines in\mathbb P^ 2 P 2 over either the reals or the complex numbers
as an algebraic plane curve, then it is an open problem to classify for all s those for which …
as an algebraic plane curve, then it is an open problem to classify for all s those for which …
Asymptotics of linear systems, with connections to line arrangements
B Harbourne - arXiv preprint arXiv:1705.09946, 2017 - arxiv.org
The main focus of these notes is recent work on linear systems in which line arrangements
play a role, including problems such as semi-effectivity, containment problems of symbolic …
play a role, including problems such as semi-effectivity, containment problems of symbolic …