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Algebraic boundaries of SO(2)-orbitopes

Type of Publication: Journal article
Author: Sinn, Rainer
Year of publication: 2013
Published in: Discrete & Computational Geometry ; 50 (2013), 1. - pp. 219-235. - ISSN 0179-5376. - eISSN 1432-0444
DOI (citable link): https://dx.doi.org/10.1007/s00454-013-9501-5
Summary:
Let X⊂A2r be a real curve embedded into an even-dimensional affine space. We characterise when the r th secant variety to X is an irreducible component of the algebraic boundary of the convex hull of the real points X(R) of X. This fact is then applied to 4 -dimensional SO(2) -orbitopes and to the so called Barvinok–Novik orbitopes to study when they are basic closed semi-algebraic sets. In the case of 4 -dimensional SO(2) -orbitopes, we find all irreducible components of their algebraic boundary.
Subject (DDC): 510 Mathematics

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SINN, Rainer, 2013. Algebraic boundaries of SO(2)-orbitopes. In: Discrete & Computational Geometry. 50(1), pp. 219-235. ISSN 0179-5376. eISSN 1432-0444. Available under: doi: 10.1007/s00454-013-9501-5

@article{Sinn2013Algeb-26409, title={Algebraic boundaries of SO(2)-orbitopes}, year={2013}, doi={10.1007/s00454-013-9501-5}, number={1}, volume={50}, issn={0179-5376}, journal={Discrete & Computational Geometry}, pages={219--235}, author={Sinn, Rainer} }

eng 2014-02-18T13:52:16Z terms-of-use 2013 Sinn, Rainer Sinn, Rainer Algebraic boundaries of SO(2)-orbitopes 2014-02-18T13:52:16Z Let X⊂A<sup>2r</sup> be a real curve embedded into an even-dimensional affine space. We characterise when the r th secant variety to X is an irreducible component of the algebraic boundary of the convex hull of the real points X(R) of X. This fact is then applied to 4 -dimensional SO(2) -orbitopes and to the so called Barvinok–Novik orbitopes to study when they are basic closed semi-algebraic sets. In the case of 4 -dimensional SO(2) -orbitopes, we find all irreducible components of their algebraic boundary. Discrete & Computational Geometry ; 50 (2013), 1. - S. 219-235

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