Algebraic boundaries of SO(2)-orbitopes

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2013
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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.

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ISO 690SINN, Rainer, 2013. Algebraic boundaries of SO(2)-orbitopes. In: Discrete & Computational Geometry. 2013, 50(1), pp. 219-235. ISSN 0179-5376. eISSN 1432-0444. Available under: doi: 10.1007/s00454-013-9501-5
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@article{Sinn2013Algeb-26409,
  year={2013},
  doi={10.1007/s00454-013-9501-5},
  title={Algebraic boundaries of SO(2)-orbitopes},
  number={1},
  volume={50},
  issn={0179-5376},
  journal={Discrete & Computational Geometry},
  pages={219--235},
  author={Sinn, Rainer}
}
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