This is not the latest version of this item. The latest version can be found at: https://kops.unikonstanz.de/handle/123456789/23348.2
Type of Publication:  Preprint 
Author:  Scheiderer, Claus 
Year of publication:  2012 
ArXivID:  arXiv:1208.3865 
Summary: 
We prove that the closed convex hull of any onedimensional semialgebraic subset of R^n has a semidefinite representation, meaning that it can be written as a linear projection of the solution set of some linear matrix inequality. This is proved by an application of the moment relaxation method. Given a nonsingular affine real algebraic curve C and a compact semialgebraic subset K of its Rpoints, the preordering P(K) of all regular functions on C that are nonnegative on K is known to be finitely generated. We prove that P(K) is stable, which means that uniform degree bounds exist for representing elements of P(K). We also extend this last result to the case where K is only virtually compact. The main technical tool for the proof of stability is the archimedean localglobal principle. As a consequence from our results we establish the HeltonNie conjecture in dimension two: Every convex semialgebraic subset of R^2 has a semidefinite representation.

Subject (DDC):  510 Mathematics 
Bibliography of Konstanz:  Yes 
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SCHEIDERER, Claus, 2012. Semidefinite representation for convex hulls of real algebraic curves
@unpublished{Scheiderer2012Semid23348, title={Semidefinite representation for convex hulls of real algebraic curves}, year={2012}, author={Scheiderer, Claus} }