Nonnegativity certificates on real algebraic surfaces
Algebraic Geometry
2024-09-16 v1
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.
Cite
@article{arxiv.2409.08834,
title = {Nonnegativity certificates on real algebraic surfaces},
author = {Grigoriy Blekherman and Rainer Sinn and Gregory G. Smith and Mauricio Velasco},
journal= {arXiv preprint arXiv:2409.08834},
year = {2024}
}
Comments
34 pages