Singularities and Genus of the k-Ellipse

Journal of Symbolic Computation（2020）

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摘要

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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关键词

Algebraic curves,Semidefinite programming,Algebraic geometry

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