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

Shinzo Bannai , Ryosuke Masuya, Taketo Shirane , Hiro-o Tokunaga, and EmikoYorisaki

In the study of plane curves, one of the problems is to classify the embedded topology of plane curves in the complex projective plane that have a given fixed combinatorial type, where the combinatorial type of a plane curve is data equivalent to the embedded topology in its tubular
neighborhood. A pair of plane curves with the same combinatorial type but distinct embedded
topology is called a Zariski pair. In this paper, we consider Zariski pairs consisting of 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 ≥2 that consist of reducible curves having two conics and 2m+2 lines as irreducible components.

Canadian Mathematical Bulletin 

Cambridge University Press

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0008-4395

http://dx.doi.org/10.4153/S0008439524000481

http://dx.doi.org/10.4153/S0008439524000481