Singular plane curves: freeness and combinatorics

authored by

Michael Cuntz, Piotr Pokora

Abstract

In this paper we focus on various aspects of singular complex plane curves, mostly in the context of their homological properties and the associated combinatorial structures. We formulate some challenging open problems that can point to new directions in research, for example by introducing weak Ziegler pairs of curve arrangements. Moreover, we construct new examples of different Ziegler pairs, in both the classical and the weak sense, and present new geometric approaches to construction problems of singular plane curves.

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

External Organisation(s)

University of the National Education Commission Krakow

Type

Article

Journal

Innovations in Incidence Geometry

Volume

22

Pages

47–65

No. of pages

19

ISSN

2640-7337

Publication date

28.05.2025

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Geometry and Topology

Electronic version(s)

https://doi.org/10.2140/iig.2025.22.47 (Access: Closed)
https://doi.org/10.48550/arXiv.2403.13377 (Access: Open)