Author

Piotr Pokora

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Preprint Sep 2026

A generalized Terao Conjecture for line arrangements

For a line arrangement $\mathcal{A} \colon f=0$ in $\mathbb{P}^2$, let $\nu(\mathcal{A})$ be the maximal dimension of a graded piece of the Jacobian module of $f$. We study the conjecture that $\nu(\mathcal{A})$ depends only on the intersection lattice of $\mathcal{A}$. It is known that $\mathcal{A}$ is free if and onl...

A. Dimca, Piotr Pokora · 1 citation · ⚡1

Preprint Sep 2026

Demailly's Inequality for Finite Sets of Points in Positive Characteristic

Let $k$ be an algebraically closed field of characteristic $p>0$, $n\ge1$, and let $X\subset \mathbb P^n_k$ be a finite nonempty set of distinct points with the defining ideal $I=I(X)$. We give a proof of Demailly's inequality in positive characteristic. The argument is based on the Frobenius--Hasse derivative method u...

Piotr Pokora, T. Szemberg · 0 citations

Preprint Aug 2026

Simplicial arrangements in real projective three-space revisited

In this paper we study irreducible simplicial arrangements of projective planes in $\mathbb{P}^{3}(\mathbb{R})$ from combinatorial and projective geometry viewpoints. We first formulate a simpliciality criterion in terms of incidences between rank-two and rank-three flats, together with equivalent formulations using fa...

Marek Janasz, Piotr Pokora · 0 citations