2020/10/21 by Brysiewicz, Taylor, Fevola, Claudia, Sturmfels, Bernd
#Algebraic Geometry (math.AG) #Computational Geometry (cs.CG) #FOS: Computer and information sciences #FOS: Mathematics
paper · doi:10.48550/arxiv.2010.10879
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.