36 citations · 276 across the 69 of their papers we have counts for
7 papers · 1 filter
On the geography of log-surfaces
Bartosz Naskręcki, Piotr Pokora
This survey focuses on the geometric problem of log-surfaces, which are pairs consisting of a smooth projective surface and a reduced non-empty boundary divisor. In the first part,…
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…
A new hierarchy for complex plane curves
Takuro Abe, Alexandru Dimca, Piotr Pokora
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. Cu…
On the numerical Terao's conjecture and Ziegler pairs for line arrangements
Lukas Kühne, Dante Luber, Piotr Pokora
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 consi…
Defect of irreducible plane curves with simple singularities
Piotr Pokora
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 fr…
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…