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arXiv · 2010.10879

Tangent Quadrics in Real 3-Space

Taylor Brysiewicz·Claudia Fevola·Bernd Sturmfels
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Abstract

We examine quadratic surfaces in 3-space that are tangent to nine given figures. These figures can be points, lines, planes or quadrics. The numbers of tangent quadrics were determined by Hermann Schubert in 1879. We study the associated systems of polynomial equations, also in the space of complete quadrics, and we solve them using certified numerical methods. Our aim is to show that Schubert's problems are fully real.

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Taylor Brysiewicz, Claudia Fevola, Bernd Sturmfels. 2020-10-21. Tangent Quadrics in Real 3-Space. https://arxiv.org/abs/2010.10879

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