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arXiv · 1908.01414

Singularities and Genus of the k-Ellipse

Yuhan Jiang·Weiqiao Han
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Abstract

A k-ellipse is a plane curve consisting of all points whose distances from k fixed foci sum to a constant. We determine the singularities and genus of its Zariski closure in the complex projective plane. The paper resolves an open problem stated by Nie, Parrilo and Sturmfels in 2008.

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Yuhan Jiang, Weiqiao Han. 2019-08-04. Singularities and Genus of the k-Ellipse. https://arxiv.org/abs/1908.01414

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