2004/02/24 by Ciprian Borcea, Ciprian S. Borcea, Borcea, Ciprian +6
Computer Science · Mathematics · #14N05 (Primary) 14J28 #14P05 (Secondary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Mathematics and Applications #Polynomial and algebraic computation #math.AG #msc:14J28 #msc:14N05 #msc:14P05
paper · pdf · doi:10.48550/arxiv.math/0402394
50 pages
arxiv created 2004/02/24 · openalex publication_date 2004/02/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the variety of common tangents for up to four quadric surfaces in projective three-space, with particular regard to configurations of four quadrics admitting a continuum of common tangents. We formulate geometrical conditions in the projective space defined by all complex quadric surfaces which express the fact that several quadrics are tangent along a curve to one and the same quadric of rank at least three, and called, for intuitive reasons: a basket. Lines in any ruling of the latter will be common tangents. These considerations are then restricted to spheres in Euclidean three-space, and result in a complete answer to the question over the reals: ``When do four spheres allow infinitely many common tangents?''.