Year: 2025
Type: article
Abstract: In this note, we examine the arrangements of lines and configurations of points in $$\mathbb {P}^2(\mathbb {C})$$ that emerge from Fermat (or von Dyck) and Komiya–Kuribayashi quartics. These quartics are characterized by having the maximum number of lines of maximal tangency, that is, lines for which the intersection multiplicity at the tangency point is equal to the degree of the curve. Additionally, we delve into the study of sextactic points on these quartics — points at which there exists a conic with the curve having a local intersection multiplicity of at least 6, which is one more than that observed at a general point — alongside the related configurations of conics.
Source: Periodica Mathematica Hungarica
Authors: Łukasz Merta, Marcin Zieliński
Institution: Uniwersytet Komisji Edukacji Narodowej w Krakowie
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W4410738262