3 papers
math.AG2026
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…
math.AG2025
On free line arrangements with double, triple and quadruple points
Marek Janasz, Izabela LeÅniak
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…
math.AG2025
On the existence of maximizing curves of odd degrees
Marek Janasz, Izabela LeÅniak
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…