Poncelet's closure theorem and the embedded topology of conic-line arrangements

Poncelet's closure theorem and the embedded topology of conic-line arrangements

In this paper, we consider conic-line arrangements that arise from Poncelet's closure theorem. We study unramified double covers of the union of two conics, that are induced by a $2m$-sided Poncelet transverse. As an application, we show the existence of families of Zariski pairs of degree $2m+...

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Hauptverfasser: Bannai, Shinzo, Masuya, Ryosuke, Shirane, Taketo, Tokunaga, Hiro-o, Yorisaki, Emiko
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Algebraic Geometry
Mathematics - Combinatorics
Mathematics - Geometric Topology
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Zusammenfassung:In this paper, we consider conic-line arrangements that arise from Poncelet's closure theorem. We study unramified double covers of the union of two conics, that are induced by a $2m$-sided Poncelet transverse. As an application, we show the existence of families of Zariski pairs of degree $2m+6$ for $m\geq 2$ that consist of reducible curves having two conics and $2m+2$ lines as irreducible components.
DOI:10.48550/arxiv.2312.01868