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：

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k椭圆的奇异性和类

甲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。