Nonnegativity certificates on real algebraic surfaces

2024/09/13 by Grigoriy Blekherman, Rainer Sinn, Blekherman, Grigoriy +5
Computer Science · Engineering · Mathematics · #12D15 #14J26 #14P05 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #FOS: Mathematics #History and Theory of Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2409.08834

openalex publication_date 2024/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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