Related papers: Minimal plus-one generated line arrangements with …
We classify the irreducible projective representations of symmetric and alternating groups of minimal possible and second minimal possible dimensions, and get a lower bound for the third minimal dimension. On the way we obtain some new…
The complete classification of (3,3)-nets and of (3,4)-nets with only double and triple points is given. Up to lattice isomorphism, there are exactly 3 effective possibilities in each case, and some of these provide new examples of…
We study the minimum number of minimal codewords in linear codes from the point of view of projective geometry. We derive bounds and in some cases determine the exact values. We also present an extension to minimal subcode supports.
We construct stationary perturbations of a specific minimal surface with a circle of triple junctions in $\mathbb{R}^2 \times \mathbb{S}^1$, that satisfy given boundary data.
The main purpose of this survey is to provide an introduction, algebro-topological in nature, to Hirzebuch-type inequalities for plane curve arrangements in the complex projective plane. These inequalities gain more and more interest due to…
Given a set of points in the plane, we are interested in matching them with straight line segments. We focus on perfect (all points are matched) non-crossing (no two edges intersect) matchings. Apart from the well known MinMax variation,…
In this survey on combinatorial properties of triangulated manifolds we discuss various lower bounds on the number of vertices of simplicial and combinatorial manifolds. Moreover, we give a list of all known examples of vertex-minimal…
Consider a real line equipped with a (not necessarily intrinsic) distance. We deal with the minimum-weight perfect matching problem for a complete graph whose points are located on the line and whose edges have weights equal to distances…
We show a one-to-one correspondence between arrangements of d lines in the projective plane, and lines in P^{d-2}. We apply this correspondence to classify (3,q)-nets over the complex numbers for all q<=6. When q=6, we have twelve possible…
A recent paper showed how to find sets of finite affine or projective planes constructed on a common set of points, so that lines of one plane meet lines of a different plane in at most two points. In this paper, those results are…
In this paper we describe all possible reduced complete intersection sets of points on Veronese surfaces. We formulate a conjecture for the general case of complete intersection subvarieties of any dimension and we prove it in the case of…
A strong blocking set in a finite projective space is a set of points that intersects each hyperplane in a spanning set. We provide a new graph theoretic construction of such sets: combining constant-degree expanders with asymptotically…
We construct two combinatorially equivalent line arrangements in the complex projective plane such that the fundamental groups of their complements are not isomorphic. The proof uses a new invariant of the fundamental group of the…
In this paper we focus on minimal Besicovitch arrangements to highlight some of their properties. An appropriate probability space enables us to find again in an elegant way some straightforward equalities associated with these…
We show that a line arrangement in the complex projective plane supports a nontrivial resonance variety if and only if it is the underlying arrangement of a "multinet," a multi-arrangement with a partition into three or more equinumerous…
We study triangle decompositions of graphs. We consider constructions of classes of graphs where every edge lies on a triangle and the addition of the minimum number of multiple edges between already adjacent vertices results in a strongly…
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…
We give restrictions on the weak combinatorics of line arrangements with singular points of odd multiplicity using topological arguments on locally-flat spheres in 4-manifolds. As a corollary, we show that there is no line arrangement…
We study effective versions of unlikely intersections of images of torsion points of elliptic curves on the projective line.
We prove two conjectures on weighted complete intersections and give the complete classification of threefold weighted complete intersections in weighted projective space that are canonically or anticanonically embedded.