9 citations · 13 across the 15 of their papers we have counts for
15 papers
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 boundedness of some real line arrangements of type at most one
Marek Janasz
In this note, we show that real line arrangements of type at most one, admitting only intersection points of multiplicity at most five, satisfy certain boundedness properties. In p…
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…
Unexpected hypersurfaces of type
Marek Janasz, Grzegorz Malara, Halszka Tutaj-Gasińska
Unexpected hypersurfaces arise when vanishing in points of a set and higher-order vanishing along a general linear subspace fails to impose the expected number of independent c…
On free line arrangements with double, triple and quadruple points
Marek Janasz, Izabela Leśniak
We show that there are only finitely many combinatorial types of free real line arrangements with only double, triple and quadruple intersection points, and we enlist all admissibl…
On homological properties of some Cynk-Szemberg octic hyperplane arrangements
Marek Janasz, Piotr Pokora
In this paper we study Cynk-Szemberg octic hyperplane arrangements from the perspective of homological properties of their derivation modules. In particular, we define the notion o…
On the existence of maximizing curves of odd degrees
Marek Janasz, Izabela Leśniak
In this paper we provide the non-existence criterion for the so-called maximizing curves of odd degrees. Furthermore, in the light of our criterion, we define a new class of plane…
On symmetric plane quartic curves
Marek Janasz
In the present paper we study the geometry of plane quartics with large automorphism groups. We show results devoted to smooth plane quartics that are invariant under the action of…
On the containment problem and sporadic simplicial line arrangements
Marek Janasz
In the paper we present two examples of inductively free sporadic simplicial arrangements of 31 lines that are non-isomorphic, which allow us to answer negatively questions on the…
On arrangements of smooth plane quartics and their bitangents
Marek Janasz, Piotr Pokora, Marcin Zieliński
In the present paper, we revisit the geometry of smooth plane quartics and their bitangents from several perspectives. First, we study in detail the weak combinatorics of arrangeme…
A note on free determinantal hypersurface arrangements in
Marek Janasz, Paulina Wiśniewska
In the present note we study determinantal arrangements constructed with use of the -minors of a generic matrix of indeterminates. In particular, we show that certa…
On the nearly free simplicial line arrangements with up to lines
Marek Janasz
In the present note we provide a complete classification of nearly free (and not free simultaneously) simplicial arrangements of lines.
On plane conic arrangements with nodes and tacnodes
Alexandru Dimca, Marek Janasz, Piotr Pokora
In the present paper, we study arrangements of smooth plane conics having only nodes and tacnodes as the singularities. We provide an interesting estimation on the number of nodes…
On Seshadri constants and point-curve configurations
Marek Janasz, Piotr Pokora
In the note we study the multipoint Seshadri constants of centered at singular loci of certain curve arrangements in the complex proj…
New phenomena in the containment problem for simplicial arrangements
Marek Janasz, Magdalena Lampa-Baczyńska, Grzegorz Malara
In this note we consider two simplicial arrangements of lines and ideals of intersection points of these lines. There are intersection points in both cases and the number…