English

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

R2 v1 2026-06-28T18:43:43.528Z