36 citations · 276 across the 69 of their papers we have counts for
10 papers · 1 filter
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 K-stability of blown up along a quintic elliptic curve
Ivan Cheltsov, Piotr Pokora
In this note, we study K-stability of smooth Fano threefolds that can be obtained by blowing up the three-dimensional projective space along a smooth elliptic curve of degree five.
On plus-one generated conic-line arrangements with simple singularities
Anca Măcinic, Piotr Pokora
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…
On arrangements of smooth plane quartics and their bitangents
Marek Janasz, Piotr Pokora, Marcin Zieliński
In the present paper, we revisit the geometry of smooth plane quartics and their bitangents from several perspectives. First, we study in detail the weak combinatorics of arrangeme…
On the Alexander polynomials of conic-line arrangements
Alexandru Dimca, Piotr Pokora, Gabriel Sticlaru
In the present paper we compute Alexander polynomials for certain classes of conic-line arrangements in the complex projective plane which are related to pencils. We prove two gene…
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…
Construction of free curves by adding lines to a given curve
Alexandru Dimca, Giovanna Ilardi, Piotr Pokora +1
In the present note we construct new families of free plane curves starting from a curve and adding high order inflectional tangent lines of , lines joining the singularitie…