16 citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- AGH University of KrakowPL5 papers
- Deutsches Elektronen-Synchrotron DESYDE4 papers
- GSI Helmholtz Centre for Heavy Ion ResearchDE4 papers
- Heidelberg UniversityDE4 papers
- High Energy Accelerator Research OrganizationJP4 papers
- Institute of Nuclear Physics, Polish Academy of SciencesPL4 papers
- Institute of Particle and Nuclear Studies4 papers
- Istituto Nazionale di Fisica Nucleare, Sezione di BolognaIT4 papers
- Istituto Nazionale di Fisica Nucleare, Sezione di PadovaIT4 papers
- Istituto Nazionale di Fisica Nucleare, Sezione di TorinoIT4 papers
- Max Planck Institute for PhysicsDE4 papers
- National Centre for Nuclear ResearchPL4 papers
15 papers · 1 filter
On combinatorial bounds for the total Tjurina numbers of certain curves and surfaces with isolated singularities
Piotr Pokora
We investigate combinatorial bounds for the total Tjurina numbers of some plane curve arrangements. Focusing on arrangements of lines and conics in that admit only o…
On plus-one generated arrangements of plane conics
Artur Bromboszcz, Bartosz Jarosławski, Piotr Pokora
In this paper, we examine the combinatorial properties of conic arrangements in the complex projective plane that possess certain quasi-homogeneous singularities. First, we introdu…
Free line arrangements with low maximal multiplicity
Alexandru Dimca, Lukas Kühne, Piotr Pokora
Let $\A$ be a free arrangement of lines in the complex projective plane, with exponents . Let be the maximal multiplicity of points in $\A$. In this note, we d…
On homological properties of some Cynk-Szemberg octic hyperplane arrangements
Marek Janasz, Piotr Pokora
In this paper we study Cynk-Szemberg octic hyperplane arrangements from the perspective of homological properties of their derivation modules. In particular, we define the notion o…
On the addition technique for Betti and Poincaré polynomials of plane curves
Piotr Pokora
Using the addition technique, we present polynomial identities for the Betti and Poincaré polynomials of reduced plane curves.
On Poincaré polynomials for plane curves with quasi-homogeneous singularities
Piotr Pokora
We define a combinatorial object that can be associated with any conic-line arrangement with ordinary singularities, which we call the combinatorial Poincaré polynomial. We prove a…
Minimal plus-one generated line arrangements with double and triple intersection points
Artur Bromboszcz
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…
Construction of free arrangements using point-line operators
Piotr Pokora, Xavier Roulleau
We construct new examples of free curve arrangements in the complex projective plane using point-line operators recently defined by the second author. In particular, we construct a…
Singular plane curves: freeness and combinatorics
Michael Cuntz, Piotr Pokora
In this paper we focus on various aspects of singular complex plane curves, mostly in the context of their homological properties and the associated combinatorial structures. We fo…
Arrangements of inflectional lines, hyperosculating conics, and plane cubics
Artur Bromboszcz
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 arrang…
Freeness of arrangements of lines and one conic with ordinary quasi-homogeneous singularities
Piotr Pokora
The main purpose of the present paper is to provide a partial classification, performed with respect the weak-combinatorics, of free arrangements consisting of lines and one smooth…
Bounds for characteristic numbers of conic-line arrangements in the plane
Rita Pardini, Piotr Pokora
The main aim of the note is to provide an upper-bound for the characteristic number of conic-line arrangements with ordinary singularities in the complex projective plane.
Construction of free curves by adding osculating conics to a given cubic curve
Alexandru Dimca, Giovanna Ilardi, Grzegorz Malara +1
In the present article we construct new families of free and nearly free curves starting from a plane cubic curve and adding some of its hyperosculating conics. We present resu…
Addition-deletion results for plus-one generated curves
Anca Măcinic, Piotr Pokora
In the recent paper A. Dimca proves that when one adds to or deletes a line from a free curve the resulting curve is either free or plus-one generated. We prove the converse statem…
On free and nearly free arrangements of conics admitting certain singularities
Piotr Pokora
The main purpose of this paper is to provide combinatorial constraints on the constructability of free and nearly free arrangements of smooth plane conics admitting certain ${\rm A…