The purpose of this note is to provide an overview of the containment problem for symbolic
and ordinary powers of homogeneous ideals, related conjectures and examples. We focus …

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 …

The purpose of this work is to collect in one place available information on line
arrangements known in the literature as braid, monomial, Ceva or Fermat arrangement …

Abstract The Klein and Wiman configurations are highly symmetric configurations of lines in
the projective plane arising from complex reflection groups. One noteworthy property of …

We study some natural operators acting on configurations of points and lines in the plane
and remark that many interesting configurations are fixed points for these operators. We …

We consider in this paper the following questions: does the Jacobian ideal of a smooth
hypersurface have the Weak Lefschetz Property? Does the Jacobian ideal of a smooth …

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 …

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 …

Let Z be a finite set of points in the projective plane and let I= I (Z) be its homogeneous ideal.
In this paper we study the sequence α (I (m)), m= 1, 2, 3…, of initial degrees of symbolic …

Similar to the linear Harbourne constant recently introduced in, we study the elliptic-
constants of and of Abelian surfaces. We also study the Harbourne indices of curves on …