Real Algebraic and Analytic Geometry
Submission: 2009, February 20.
Let A be an excellent regular local ring of dimension two, let T be a finitely generated preordering in A, and let T' be the preordering generated by T in the completion A' of A. We study the question when the property of being saturated descends from T' to T, and establish conditions of geometric nature which allow to decide this question. As an application we classify all principal preorderings in A of degree at most 3 which are saturated. These results have direct implications for nonnegativity certificates for real polynomials on two-dimensional semi-algebraic sets.
Mathematics Subject Classification (2000): 14P99,13H05, 14P10, 32S05, 58K50.
Keywords and Phrases: Local rings, completion, preorderings, curve singularities, spaces of orderings, positive polynomials, sums of squares, real algebraic geometry.
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