2008/08/04 by Daniel Plaumann, Plaumann, Daniel
Computer Science · Mathematics · #11E25 #13J30 #14H99 #14P05 (Secondary) #14P99 (Primary) #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AC #math.AG #msc:11E25 #msc:13J30 #msc:14H99 #msc:14P05 #msc:14P99
paper · pdf · doi:10.48550/arxiv.0808.0460
v4: some corrections and improvements;
openalex publication_date 2008/08/04 · arxiv created 2009/03/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We ask whether every polynomial function that is non-negative on a real algebraic curve can be expressed as a sum of squares in the coordinate ring. Scheiderer has classified all irreducible curves for which this is the case. For reducible curves, we show how the answer depends on the configuration of the irreducible components and give complete necessary and sufficient conditions. We also prove partial results in the more general case of finitely generated preorderings and discuss applications to the moment problem for semialgebraic sets.