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Singularities and genus of the k-ellipse
Journal of Symbolic Computation ( IF 0.6 ) Pub Date : 2020-06-25 , DOI: 10.1016/j.jsc.2020.06.009
Yuhan Jiang , Weiqiao Han

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.



中文翻译:

k椭圆的奇异性和类

ķ -椭圆是由它的距离从所有点的平面曲线ķ固定焦点总和为恒定。我们确定其Zariski闭在复杂投影平面上的奇异性和类。该论文解决了Nie,Parrilo和Sturmfels在2008年提出的一个开放性问题。

更新日期:2020-06-25
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