Sums of squares and varieties of minimal degree

DOI10.1090/jams/847zbMath1388.14156arXiv1308.0751OpenAlexW1765206433MaRDI QIDQ2802075

Gregory G. Smith, Grigoriy Blekherman, Mauricio Velasco

Publication date: 25 April 2016

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1308.0751

Mathematics Subject Classification ID

Semidefinite programming (90C22) Real algebraic sets (14P05) Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) (12D15)

Related Items (24)

Sums of squares and quadratic persistence on real projective varieties ⋮ On the extreme rays of the cone of \(3\times 3\) quasiconvex quadratic forms: extremal determinants versus extremal and polyconvex forms ⋮ On the tightness of semidefinite relaxations for rotation estimation ⋮ Extreme points of Gram spectrahedra of binary forms ⋮ Approximate super-resolution of positive measures in all dimensions ⋮ New examples of extremal positive linear maps ⋮ Do Sums of Squares Dream of Free Resolutions? ⋮ A practical approach to SOS relaxations for detecting quantum entanglement ⋮ The geometry of SDP-exactness in quadratic optimization ⋮ Sampling Algebraic Varieties for Sum of Squares Programs ⋮ Causality constraints on corrections to Einstein gravity ⋮ Harmonic Hierarchies for Polynomial Optimization ⋮ Real rank boundaries and loci of forms ⋮ Gram spectrahedra ⋮ Sums of Squares and Sparse Semidefinite Programming ⋮ Multihomogeneous nonnegative polynomials and sums of squares ⋮ Sharp degree bounds for sum-of-squares certificates on projective curves ⋮ NONNEGATIVE POLYNOMIALS, SUMS OF SQUARES AND THE MOMENT PROBLEM ⋮ Gap vectors of real projective varieties ⋮ Certifying Polynomial Nonnegativity via Hyperbolic Optimization ⋮ A Linear-algebraic Proof of Hilbert’s Ternary Quartic Theorem ⋮ Blowup algebras of rational normal scrolls ⋮ Convex Algebraic Geometry of Curvature Operators ⋮ Dual Toric Codes and Polytopes of Degree One

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