Grigoriy Blekherman, Rainer Sinn, Gregory G. Smith, Mauricio Velasco
{"title":"Nonnegativity certificates on real algebraic surfaces","authors":"Grigoriy Blekherman, Rainer Sinn, Gregory G. Smith, Mauricio Velasco","doi":"arxiv-2409.08834","DOIUrl":null,"url":null,"abstract":"We introduce tools for transferring nonnegativity certificates for global\nsections between line bundles on real algebraic surfaces. As applications, we\nimprove Hilbert's degree bounds on sum-of-squares multipliers for nonnegative\nternary forms, give a complete characterization of nonnegative real forms of\ndel Pezzo surfaces, and establish quadratic upper bounds for the degrees of\nsum-of-squares multipliers for nonnegative forms on real ruled surfaces.","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":"15 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Algebraic Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.08834","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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.