Determinantal representations and Bézoutians

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2017
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Mathematische Zeitschrift. 2017, 285(1-2), pp. 445-459. ISSN 0025-5874. eISSN 1432-1823. Available under: doi: 10.1007/s00209-016-1715-9
Zusammenfassung

A major open question in convex algebraic geometry is whether all hyperbolicity cones are spectrahedral, i.e. the solution sets of linear matrix inequalities. We will use sum-of-squares decompositions of certain bilinear forms called Bézoutians to approach this problem. More precisely, we show that for every smooth hyperbolic polynomial h there is another hyperbolic polynomial q such that q⋅h has a definite determinantal representation. Besides commutative algebra, the proof relies on results from real algebraic geometry.

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510 Mathematik
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ISO 690KUMMER, Mario, 2017. Determinantal representations and Bézoutians. In: Mathematische Zeitschrift. 2017, 285(1-2), pp. 445-459. ISSN 0025-5874. eISSN 1432-1823. Available under: doi: 10.1007/s00209-016-1715-9
BibTex
@article{Kummer2017-02Deter-37954,
  year={2017},
  doi={10.1007/s00209-016-1715-9},
  title={Determinantal representations and Bézoutians},
  number={1-2},
  volume={285},
  issn={0025-5874},
  journal={Mathematische Zeitschrift},
  pages={445--459},
  author={Kummer, Mario}
}
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