Skip to Main content Skip to Navigation
Conference papers

Extreme Rays of the Hankel Spectrahedra for Ternary Forms

Abstract : Hankel spectrahedra are the dual convex cones to the cone of sums of squares of real polynomials, and we study them from the point of view of convex algebraic geometry. We show that the Zariski closure of the union of all extreme rays of Hankel spectrahedra for ternary forms is an irreducible variety of codimension 10. It is the variety of all Hankel (or middle Catalecticant) matrices of corank at least 4. We explicitly construct a rational extreme ray of maximal rank using the Cayley-Bacharach Theorem for plane curves. We work out the rank stratification of the semi-algebraic set of extreme rays of Hankel spectrahedra in the first three nontrivial cases d = 3, 4, 5. Dually, we get a characterisation of the algebraic boundary of the cone of sums of squares via projective duality theory, extending previous work of Blekherman, Hauenstein, Ottem, Ranestad, and Sturmfels.
Complete list of metadatas

https://hal.inria.fr/hal-01350771
Contributor : Alain Monteil <>
Submitted on : Monday, August 1, 2016 - 4:34:53 PM
Last modification on : Wednesday, July 31, 2019 - 3:24:16 PM

Links full text

Identifiers

  • HAL Id : hal-01350771, version 1
  • ARXIV : 1406.1873

Collections

Citation

Grigoriy Blekherman, Rainer Sinn. Extreme Rays of the Hankel Spectrahedra for Ternary Forms. MEGA'2015 (Special Issue), Jun 2015, Trento, Italy. ⟨hal-01350771⟩

Share

Metrics

Record views

77