36 citations · 276 across the 69 of their papers we have counts for
12 papers · 1 filter
Lifting negative curves from finite fields and Seshadri constants at ten points
Piotr Pokora, Tomasz Szemberg
We use finite-field calculations and mixed-characteristic deformation to construct nef divisors on very general complex blow-ups of the plane. A lifting and smoothing criterion con…
A generalized Terao Conjecture for line arrangements
Alexandru Dimca, Piotr Pokora
For a line arrangement in , let be the maximal dimension of a graded piece of the Jacobian module of . We study the conje…
Demailly's Inequality for Finite Sets of Points in Positive Characteristic
Piotr Pokora, Tomasz Szemberg
Let be an algebraically closed field of characteristic , , and let be a finite nonempty set of distinct points with the defining ideal $I=I…
Simplicial arrangements in real projective three-space revisited
Marek Janasz, Piotr Pokora
In this paper we study irreducible simplicial arrangements of projective planes in from combinatorial and projective geometry viewpoints. We first form…
On the Numerical Terao Conjecture
Piotr Pokora
We prove that the Numerical Terao Conjecture holds for even-degree conic-line arrangements having only ADE singularities. We then show that the conjecture fails in the broader quas…
A nine-line counterexample to a conjecture on the minimal degree of Jacobian relations
Alexandru Dimca, Piotr Pokora
We construct two arrangements of nine lines in the complex projective plane with isomorphic intersection lattices but with different minimal degrees of Jacobian relations. The comm…
A counterexample to Purdy's inequality for hyperplane arrangements in projective three-space
Mateusz Michałek, Piotr Pokora
We record an explicit counterexample to a refined form of Purdy's inequality for essential hyperplane arrangements in projective three-space. Let be an arrangement of…
A -configuration on the Schur quartic with logarithmic Chern slope
Bartosz Naskręcki, Piotr Pokora
Let be the Schur quartic \[ x_0^4-x_0x_1^3-x_2^4+x_2x_3^3=0. \] We exhibit a connected arrangement of lines on , defined over …
A Pascal-type construction of the Segre cubic and the Cremona--Richmond configuration
Piotr Pokora, Tomasz Szemberg
We present a Pascal-type residual construction in P^4. Starting from two quadruples of hyperplanes whose four diagonal intersection planes lie in a hyperplane, we show that the twe…
On Ziegler pairs of line arrangements: from non-existence to abundance
Alexandru Dimca, Piotr Pokora
We study Ziegler pairs of line arrangements from both numerical and homological perspectives. We distinguish classical Ziegler pairs, for which the minimal degree of a Jacobian rel…
On the Jacobian algebras of Ziegler pairs of plane arrangements
Alexandru Dimca, Piotr Pokora
We consider a Ziegler pair of plane arrangements, that is two plane arrangements and in the projective space , such that the int…
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…