Convex Hull of Two Circles in R^3 Institutional Repository Document uri icon

abstract

  • We describe convex hulls of the simplest compact space curves, reducible quartics consisting of two circles. When the circles do not meet in complex projective space, their algebraic boundary contains an irrational ruled surface of degree eight whose ruling forms a genus one curve. We classify which curves arise, classify the face lattices of the convex hulls, and determine which are spectrahedra. We also discuss an approach to these convex hulls using projective duality.

author list (cited authors)

  • Nash, E. D., Pir, A. F., Sottile, F., & Ying, L. i.

complete list of authors

  • Nash, Evan D||Pir, Ata Firat||Sottile, Frank||Ying, Li

Book Title

  • arXiv

publication date

  • December 2016