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

Preprint

No. of pages

17

Publication date

23.11.2024

Publication status

E-pub ahead of print

Electronic version(s)

https://arxiv.org/abs/2403.13377 (Access: Open)