Singularities and genus of the k-ellipse. (May 2021) - Jiang, Yuhan; Han, Weiqiao
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.