Singularities and genus of the k-ellipse. (May 2021)

• Record Type: Journal Article
• Authors: Jiang, Yuhan; Han, Weiqiao
• Is Part Of: Journal of symbolic computation. Volume 104(2021)
• Page Start: 343
• Page End: 355
• Publication Date: 2021-05
• Subjects: Algebraic curves -- Semidefinite programming -- Algebraic geometry; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2020.06.009
• Languages: English
• ISSNs: 0747-7171

Abstract

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.