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Birational models for varieties of Poncelet curves

Matei Toma
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Abstract

We consider Poncelet pairs $(S,C)$, where $S$ is a smooth conic and $C$ is a degree$-c$ plane curve having the Poncelet property with respect to $S$. We prove that for $c>4$ the projection $(S,C)\mapsto C$ is generically one-to-one and use this to describe a birational model of the variety of Poncelet curves for $c$ odd.

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Matei Toma. 1996-01-22. Birational models for varieties of Poncelet curves. https://arxiv.org/abs/alg-geom/9601002

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