Singular plane curves: freeness and combinatorics

verfasst von

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.

Organisationseinheit(en)

Institut für Algebra, Zahlentheorie und Diskrete Mathematik

Externe Organisation(en)

University of the National Education Commission Krakow

Typ

Preprint

Anzahl der Seiten

17

Publikationsdatum

23.11.2024

Publikationsstatus

Elektronisch veröffentlicht (E-Pub)

Elektronische Version(en)

https://arxiv.org/abs/2403.13377 (Zugang: Offen)