Related papers: On combinatorics of plus-one generated line arrang…
We provide a complete classification, in the language of weak-combinatorics, of minimal plus-one generated line arrangements in the complex projective plane with double and triple intersection points.
In this paper we study plus-one generated arrangements of conics and lines in the complex projective plane with simple singularities. We provide several degree-wise classification results that allow us to construct explicit examples of such…
In this paper, we examine the combinatorial properties of conic arrangements in the complex projective plane that possess certain quasi-homogeneous singularities. First, we introduce a new tool that enables us to characterize the property…
We give a geometric characterisation of plus-one generated projective line arrangements that are next-to-free. We present new succinct proofs, via associated line bundles, for some properties of plus-one generated projective line…
In this paper we construct several arrangements of lines and/or conics that are derived from the geometry of the Klein arrangement of $21$ lines in the complex projective plane.
We study the combinatorics of pseudoline arrangements in the real projective plane. Our focus lies on two classes of arrangements: simplicial arrangements and arrangements whose characteristic polynomials have only real roots. We derive…
We introduce a new class of arrangements of hyperplanes, called (strictly) plus-one generated arrangements, from algebraic point of view. Plus-one generatedness is close to freeness, i.e., plus-one generated arrangements have their…
We introduce an algorithm that exploits a combinatorial symmetry of an arrangement in order to produce a geometric reflection between two disconnected components of its moduli space. We apply this method to disqualify three real examples…
By way of Ziegler restrictions we study the relation between nearly free plane arrangements and combinatorics and we give a Yoshinaga-type criterion for plus-one generated plane arrangements.
In this paper we present a smallest possible counterexample to the Numerical Terao's Conjecture in the class of line arrangements in the complex projective plane. Our example consists of a pair of two arrangements with $13$ lines. Moreover,…
We introduce a combinatorial characterization of simpliciality for arrangements of hyperplanes. We then give a sharp upper bound for the number of hyperplanes of such an arrangement in the projective plane over a finite field, and present…
We prove that under certain combinatorial conditions, the realization spaces of line arrangements on the complex projective plane are connected. We also give several examples of arrangements with eight, nine and ten lines which have…
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 compute all isomorphism classes of simplicial arrangements in the real projective plane with up to 27 lines. It turns out that Gr\"unbaums catalogue is complete up to 27 lines except for four new arrangements with 22, 23, 24, 25 lines,…
We consider colored compositions where only some parts are allowed different colors, depending on their locations in the composition. The counting sequences are obtained through generating functions. Connections to many other combinatorial…
In the present note we provide a complete classification of nearly free (and not free simultaneously) simplicial arrangements of $d\leq 27$ lines.
In this article we give a computational study of combinatorics of the discriminantal arrangements. The discriminantal arrangements are parametrized by two positive integers n and k such that n>k. The intersection lattice of the…
Let $\A$ be a free arrangement of $d$ lines in the complex projective plane, with exponents $d_1\leq d_2$. Let $m$ be the maximal multiplicity of points in $\A$. In this note, we describe first the simple cases $d_1 \leq m$. Then we study…
We show that there are only finitely many combinatorial types of free real line arrangements with only double, triple and quadruple intersection points, and we enlist all admissible weak-combinatorics of them. Then we classify all real…
We prove Terao conjecture saying that the freeness is determined by the combinatorics for arrangements of 13 lines in the complex projective plane and that the property of being nearly free is combinatorial for line arrangements of up to 12…