Zobrazeno 1 - 10
of 143
pro vyhledávání: '"Pokora, Piotr"'
We define the type of a plane curve as the initial degree of the corresponding Bourbaki ideal. Then we show that this invariant behaves well with respect to the union of curves. The curves of type $0$ are precisely the free curves and the curves of t
Externí odkaz:
http://arxiv.org/abs/2410.11479
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 use th
Externí odkaz:
http://arxiv.org/abs/2407.07070
Autor:
Pokora, Piotr
In this note we focus on the defect of singular plane curve that was recently introduced by Dimca. Roughly speaking, the defect of a reduced plane curve measures the discrepancy from the property of being a free curve. We find some lower-bound on the
Externí odkaz:
http://arxiv.org/abs/2404.03341
Autor:
Pokora, Piotr, Roulleau, Xavier
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 new example of a conic-line arrangement with ordinary quasi-homogeneo
Externí odkaz:
http://arxiv.org/abs/2403.20024
Autor:
Pokora, Piotr
In this survey we focus on various aspects of singular complex plane curves, mostly in the context of their homological properties and the associated combinatorial structures. We formulate some demanding open problems that can indicate new directions
Externí odkaz:
http://arxiv.org/abs/2403.13377
Autor:
Pokora, Piotr
Publikováno v:
Taiwanese Journal of Mathematics (2025)
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 conic with quasi-homogeneous ordinary singularities.
Comment: Ve
Comment: Ve
Externí odkaz:
http://arxiv.org/abs/2312.13052
Autor:
Pardini, Rita, Pokora, Piotr
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.
Comment: 11 pages, comments welcome
Comment: 11 pages, comments welcome
Externí odkaz:
http://arxiv.org/abs/2312.12950
In the present article we construct new families of free and nearly free curves starting from a plane cubic curve $C$ and adding some of its hyperosculating conics. We present results that involve nodal cubic curves and the Fermat cubic. In addition,
Externí odkaz:
http://arxiv.org/abs/2311.08913
Autor:
Măcinic, Anca, Pokora, Piotr
Publikováno v:
Journal of Algebraic Combinatorics 60: 723 - 734 (2024)
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 statements, we give an additional insight into the original deletion result,
Externí odkaz:
http://arxiv.org/abs/2310.19610
Autor:
Măcinic, Anca, Pokora, Piotr
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 arrangeme
Externí odkaz:
http://arxiv.org/abs/2309.15228