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

@inproceedings{Blekherman2016SharpDB,
  title={Sharp degree bounds for sum-of-squares certificates on projective curves},
  author={Grigoriy Blekherman and Gregory G. Smith and Mauricio Velasco},
  year={2016}
}
Abstract 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… CONTINUE READING

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