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Singular plane curves: freeness and combinatorics

2025/01/01 by Cuntz, Michael, Pokora, Piotr
Mathematics · #500 | Naturwissenschaften::510 | Mathematik #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Geometric and Algebraic Topology #combinatorics #minimal free resolutions #singular plane curves

paper · doi:10.15488/20112

openalex publication_date 2025/01/01 · openalex created_date 2025/12/01 · openalex updated_date 2026/07/01

Abstract

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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