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Secants of minuscule and cominuscule minimal orbits

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2015

Autor:innen

Manivel, Laurent

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https://doi.org/10.1016/j.laa.2015.04.027
ArXiv-ID
http://arxiv.org/abs/1401.1956

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Mathematik und Statistik: Publikationen
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Linear Algebra and its Applications. Elsevier. 2015, 481, pp. 288-312. ISSN 0024-3795. eISSN 1873-1856. Available under: doi: 10.1016/j.laa.2015.04.027

Zusammenfassung

We study the geometry of the secant and tangential variety of a cominuscule and minuscule variety, e.g. a Grassmannian or a spinor variety. Using methods inspired by statistics we provide an explicit local isomorphism with a product of an affine space with a variety which is the Zariski closure of the image of a map defined by generalized determinants. In particular, equations of the secant or tangential variety correspond to relations among generalized determinants. We also provide a representation theoretic decomposition of cubics in the ideal of the secant variety of any Grassmannian.

Zusammenfassung in einer weiteren Sprache

Fachgebiet (DDC)
510 Mathematik

Schlagwörter

Grassmannian, Minuscule and cominuscule representation, Secant variety, Generalized determinant, Cumulants

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ISO 690MANIVEL, Laurent, Mateusz MICHALEK, 2015. Secants of minuscule and cominuscule minimal orbits. In: Linear Algebra and its Applications. Elsevier. 2015, 481, pp. 288-312. ISSN 0024-3795. eISSN 1873-1856. Available under: doi: 10.1016/j.laa.2015.04.027
BibTex
@article{Manivel2015Secan-52347,
  year={2015},
  doi={10.1016/j.laa.2015.04.027},
  title={Secants of minuscule and cominuscule minimal orbits},
  volume={481},
  issn={0024-3795},
  journal={Linear Algebra and its Applications},
  pages={288--312},
  author={Manivel, Laurent and Michalek, Mateusz}
}
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