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27 papers
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 counterexample to Purdy's inequality for hyperplane arrangements in projective three-space
Mateusz MichaÅek, 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 NaskrÄcki, 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 …
On -arrangements of conics and lines with ordinary singularities
Marek Janasz, Piotr Pokora
In this paper we study combinatorial aspects of reduced plane curves known as -curves. This notion is a natural generalization of maximizing plane curves, which are we…
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…
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…