Sums of squares on reducible real curves

Details Sums of squares on reducible real curves Sums of squares on reducible real curves

2008-08-04

arxiv.org/abs/0808.0460v4

Mathematics

Algebraic Geometry

v4: some corrections and improvements;

Scientific paper

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.

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