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arXiv · 2409.08834

Nonnegativity certificates on real algebraic surfaces

Grigoriy Blekherman·Rainer Sinn·Gregory G. Smith·Mauricio Velasco
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Abstract

We introduce tools for transferring nonnegativity certificates for global sections between line bundles on real algebraic surfaces. As applications, we improve Hilbert's degree bounds on sum-of-squares multipliers for nonnegative ternary forms, give a complete characterization of nonnegative real forms of del Pezzo surfaces, and establish quadratic upper bounds for the degrees of sum-of-squares multipliers for nonnegative forms on real ruled surfaces.

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Grigoriy Blekherman, Rainer Sinn, Gregory G. Smith, Mauricio Velasco. 2024-09-13. Nonnegativity certificates on real algebraic surfaces. https://arxiv.org/abs/2409.08834

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