Author:
Blekherman Grigoriy,Hauenstein Jonathan,Ottem John Christian,Ranestad Kristian,Sturmfels Bernd
Abstract
AbstractWe study the geometry underlying the difference between non-negative polynomials and sums of squares (SOS). The hypersurfaces that discriminate these two cones for ternary sextics and quaternary quartics are shown to be Noether–Lefschetz loci of K3 surfaces. The projective duals of these hypersurfaces are defined by rank constraints on Hankel matrices. We compute their degrees using numerical algebraic geometry, thereby verifying results due to Maulik and Pandharipande. The non-SOS extreme rays of the two cones of non-negative forms are parametrized, respectively, by the Severi variety of plane rational sextics and by the variety of quartic symmetroids.
Subject
Algebra and Number Theory
Reference34 articles.
1. Projective Models of K - 3 Surfaces
2. [Rez07] Reznick B. , On Hilbert’s construction of positive polynomials, Preprint (2007), arXiv:0707.2156.
3. Witness sets of projections;Hauenstein;Appl. Math. Comput.,2010
4. Convex Bodies: The Brunn–Minkowski Theory
5. Nonnegative polynomials and sums of squares
Cited by
25 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献