Common transversals and tangents to two lines and two quadrics in P^3
<|reference_start|>Common transversals and tangents to two lines and two quadrics in P^3: We solve the following geometric problem, which arises in several three-dimensional applications in computational geometry: For which arrangements of two lines and two spheres in R^3 are there infinitely many lines simultaneously transversal to the two lines and tangent to the two spheres?   We also treat a generalization of this problem to projective quadrics: Replacing the spheres in R^3 by quadrics in projective space P^3, and fixing the lines and one general quadric, we give the following complete geometric description of the set of (second) quadrics for which the 2 lines and 2 quadrics have infinitely many transversals and tangents: In the nine-dimensional projective space P^9 of quadrics, this is a curve of degree 24 consisting of 12 plane conics, a remarkably reducible variety.<|reference_end|>
@article{megyesi2002common,
    title={Common transversals and tangents to two lines and two quadrics in P^3},
    author={G'abor Megyesi (UMIST), Frank Sottile (U Massachusetts, Amherst),
  Thorsten Theobald (Technische Universit"at M"unchen)},
    journal={arXiv preprint arXiv:math/0206044},
    year={2002},
    archivePrefix={arXiv},
    eprint={math/0206044},
    primaryClass={math.AG cs.CG math.AC}
}