Sharp degree bounds for sum-of-squares certificates on projective curves

Grigoriy Blekherman, Gregory G. Smith, Mauricio Velasco

Producción científica: Contribución a una revistaArtículorevisión exhaustiva

6 Citas (Scopus)

Resumen

Given a real projective curve with homogeneous coordinate ring R and a nonnegative homogeneous element f∈R, we bound the degree of a nonzero homogeneous sum of squares g∈R such that the product fg is again a sum of squares. Better yet, our degree bounds only depend on geometric invariants of the curve and we show that there exist smooth curves and nonnegative elements for which our bounds are sharp. We deduce the existence of a multiplier g from a new Bertini Theorem in convex algebraic geometry and prove sharpness by deforming rational Harnack curves on toric surfaces. Our techniques also yield similar bounds for multipliers on surfaces of minimal degree, generalizing Hilbert's work on ternary forms.

Idioma originalInglés
Páginas (desde-hasta)61-86
Número de páginas26
PublicaciónJournal des Mathematiques Pures et Appliquees
Volumen129
DOI
EstadoPublicada - set. 2019
Publicado de forma externa

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