English

Smooth Hyperbolicity Cones are Spectrahedral Shadows

Optimization and Control 2012-08-03 v1 Algebraic Geometry

Abstract

Hyperbolicity cones are convex algebraic cones arising from hyperbolic polynomials. A well-understood subclass of hyperbolicity cones is that of spectrahedral cones and it is conjectured that every hyperbolicity cone is spectrahedral. In this paper we prove a weaker version of this conjecture by showing that every smooth hyperbolicity cone is the linear projection of a spectrahedral cone, that is, a spectrahedral shadow.

Keywords

Cite

@article{arxiv.1208.0441,
  title  = {Smooth Hyperbolicity Cones are Spectrahedral Shadows},
  author = {Tim Netzer and Raman Sanyal},
  journal= {arXiv preprint arXiv:1208.0441},
  year   = {2012}
}
R2 v1 2026-06-21T21:45:11.205Z