实代数曲面上的非负性证书

arXiv - MATH - Algebraic Geometry Pub Date : 2024-09-13 DOI:arxiv-2409.08834

Grigoriy Blekherman, Rainer Sinn, Gregory G. Smith, Mauricio Velasco

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引用次数: 0

摘要

我们介绍了在实代数曲面上的线束之间转移全局剖分的非负性证书的工具。作为应用，我们改进了希尔伯特关于非负非形式的平方和乘数的度界，给出了德尔佩佐曲面的非负实形式的完整表征，并建立了实规则曲面上非负形的平方和乘数的二次上限。

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Nonnegativity certificates on real algebraic surfaces

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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arXiv - MATH - Algebraic Geometry

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