Convex Hull of Two Circles in R^3
Algebraic Geometry
2017-01-24 v2
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.
Cite
@article{arxiv.1612.09382,
title = {Convex Hull of Two Circles in R^3},
author = {Evan D. Nash and Ata Firat Pir and Frank Sottile and Li Ying},
journal= {arXiv preprint arXiv:1612.09382},
year = {2017}
}
Comments
20 pages, many color .eps pictures