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arXiv · 1401.1956

Secants of minuscule and cominuscule minimal orbits

Laurent Manivel·Mateusz Michałek
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Abstract

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.

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Laurent Manivel, Mateusz Michałek. 2014-01-09. Secants of minuscule and cominuscule minimal orbits. https://doi.org/10.1016/j.laa.2015.04.027

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