Sums of squares on real algebraic curves

@article{Scheiderer2003SumsOS,
  title={Sums of squares on real algebraic curves},
  author={Claus Scheiderer},
  journal={Mathematische Zeitschrift},
  year={2003},
  volume={245},
  pages={725-760}
}
Abstract.Given an affine algebraic variety V over ℝ with real points V(ℝ) compact and a non-negative polynomial function f∈ℝ[V] with finitely many real zeros, we establish a local-global criterion for f to be a sum of squares in ℝ[V]. We then specialize to the case where V is a curve. The notion of virtual compactness is introduced, and it is shown that in the local-global principle, compactness of V(ℝ) can be relaxed to virtual compactness. The irreducible curves on which every non-negative… CONTINUE READING
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