English

Tangent Quadrics in Real 3-Space

Algebraic Geometry 2021-05-20 v2 Computational Geometry

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.

Keywords

Cite

@article{arxiv.2010.10879,
  title  = {Tangent Quadrics in Real 3-Space},
  author = {Taylor Brysiewicz and Claudia Fevola and Bernd Sturmfels},
  journal= {arXiv preprint arXiv:2010.10879},
  year   = {2021}
}

Comments

13 pages

R2 v1 2026-06-23T19:31:01.206Z