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Singular plane curves:
freeness and combinatorics
Michael Cuntz and Piotr Pokora |
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Vol. 22 (2025), No. 1-2, 47–65
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Abstract |
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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. |
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Keywords
singular plane curves, minimal free resolutions,
combinatorics
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Mathematical Subject Classification
Primary: 14N20, 32S25
Secondary: 14N25, 51A45, 51B05
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Milestones
Received: 28 November 2024
Revised: 28 April 2025
Accepted: 18 May 2025
Published: 28 May 2025
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Authors |
| Michael Cuntz | |
| Institut für Algebra, Zahlentheorie
und Diskrete Mathematik Leibniz Universität Hannover Hannover Germany |
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| Piotr Pokora | |
| Department of Mathematics University of the National Education Commission Krakow Poland |
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| © 2025 MSP (Mathematical Sciences Publishers). |
