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 …

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 …

Chudnovsky's conjecture and the stable Harbourne–Huneke containment

S Bisui, E Grifo, H Hà - … of the American Mathematical Society, Series B, 2022 - ams.org
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 …

Expected resurgences and symbolic powers of ideals

E Grifo, C Huneke, V Mukundan - Journal of the London …, 2020 - Wiley Online Library
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 …

[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 …

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 …

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 …

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 …

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 …

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 …