Albrecht Hess, A group theoretic interpretation of Poncelet's theorem, part 2: the complex case,
Forum Geometricorum, 17 (2017) 255--272.

Abstract. Poncelet's theorem about polygons that are inscribed in a conic and at the same time circumscribe another one has a greater companion, in which different conics touch the sides of the polygon, while all conics belong to a fixed pencil. In the first part of these investigations on Poncelet's theorem (Hess et al, Forum. Geom., 16 (2016) 381--395) the case of a pencil of circles in the real plane was analyzed. It was shown that the question of whether `circuminscribed' polygons exist for every starting point can be decided by considering the action of a group. As a continuation of this work we now examine the case of a pencil of conics in the complex plane. It will be shown that in this case the answer to the same question about the existence of a continuous family of `circuminscribed' polygons depends on the addition of an elliptic curve.

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