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• W2964027626 abstract "A celebrated result by Hilbert says that every real nonnegative ternary quartic is a sum of three squares. We show more generally that every nonnegative quadratic form on a real projective variety $X$ of minimal degree is a sum of $dim(X)+1$ squares of linear forms. This strengthens one direction of a recent result due to Blekherman, Smith, and Velasco. Our upper bound is the best possible, and it implies the existence of low-rank factorizations of positive semidefinite bivariate matrix polynomials and representations of biforms as sums of few squares. We determine the number of equivalence classes of sum-of-squares representations of general quadratic forms on surfaces of minimal degree, generalizing the count for ternary quartics by Powers, Reznick, Scheiderer, and Sottile." @default.
• W2964027626 created "2019-07-30" @default.
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• W2964027626 date "2017-06-18" @default.
• W2964027626 modified "2023-09-25" @default.
• W2964027626 title "Low-Rank Sum-of-Squares Representations on Varieties of Minimal Degree" @default.
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• W2964027626 doi "https://doi.org/10.1093/imrn/rnx113" @default.
• W2964027626 hasPublicationYear "2017" @default.
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