Related papers: Minimal plus-one generated line arrangements with …

Let $S$ be a finite set of points in the plane and let $\mathcal{T}(S)$ be the set of intersection points between pairs of lines passing through any two points in $S$. We characterize all configurations of points $S$ such that iteration of…

We prove the existence of complexified real arrangements with the same combinatorics but different embeddings in the complex projective plane. Such pair of arrangements has an additional property: they admit conjugated equations on the ring…

We study combinatorial parameters of a recently introduced bootstrap percolation problem in finite projective planes. We present sharp results on the size of the minimum percolating sets and the maximal non-percolating sets. Additional…

In this paper, we construct an infinite series of line arrangements in characteristic two, each featuring only triple intersection points. This finding challenges the existing conjecture that suggests the existence of only a finite number…

We prove that the topological complexity of (a motion planning algorithm on) the complement of generic complex essential hyperplane arrangement of $n$ hyperplanes in an $r$-dimensional linear space is min$\{n+1,2r\}$.

This is a short note on various results about the combinatorial properties of line arrangements in terms of the Chern numbers of the corresponding log surfaces. This resembles the study of the geography of surfaces of general type. We prove…

A widely investigated subject in combinatorial geometry, originated from Erd\H{o}s, is the following. Given a point set $P$ of cardinality $n$ in the plane, how can we describe the distribution of the determined distances? This has been…

We construct a class of super-reflexive complementably minimal spaces, and study uniformly convex distortions of the norm on Hilbert space by using methods of complex interpolation.

We give local conditions at the infinite places of a number field K ensuring that the intersection of n quadrics in projective N-space over K, N >> n, satisfies weak approximation.

We describe a new infinite family of line arrangements in the projective plane with only triple points singularities and recover previously known examples.

Given a factorable function f, we propose a procedure that constructs a concave underestimator of f that is tight at a given point. These underestimators can be used to generate intersection cuts. A peculiarity of these underestimators is…

We present a proof of the Harbourne-Hirschowitz conjecture for linear systems with base points of multiplicity seven or less. This proof uses a well-known degeneration of the projective plane, as well as a combinatorial technique that…

Using linear projections one gets new inequalities for the successive minima of the lattice of sections of an hermitian line bundle on an arithmetic surface.

We describe a method for generating minimal hard prime surface-link diagrams. We extend the known examples of minimal hard prime classical unknot and unlink diagrams up to three components and generate figures of all minimal hard prime…

Let A be a line arrangement in the complex projective plane CP2. We define and describe the inclusion map of the boundary manifold --the boundary of a close regular neighborhood of A-- in the exterior of the arrangement. We obtain two…

We consider hyperplane arrangements generated by generic points and study their intersection lattices. These arrangements are known to be equivalent to discriminantal arrangements. We show a fundamental structure of the intersection…

In the present note we study some arrangements of inflectional lines, hyperosculating conics, and a nodal plane cubic that are free. Moreover, we study weak combinatorics of arrangements consisting of lines, conics, and elliptic curves…

Questions that seek to determine whether a hyperplane arrangement property, be it geometric, arithmetic or topological, is of a combinatorial nature (that is determined by the intersection lattice) are abundant in the literature. To tackle…

We classify the solutions to an overdetermined elliptic problem in the plane in the finite connectivity case. This is achieved by establishing a one-to-one correspondence between the solutions to this problem and a certain type of minimal…

A weak pseudoline arrangement is a topological generalization of a line arrangement, consisting of curves topologically equivalent to lines that cross each other at most once. We consider arrangements that are outerplanar---each crossing is…