Secants of minuscule and cominuscule minimal orbits

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 t...

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Bibliographic Details
Published in:	Linear algebra and its applications Vol. 481; pp. 288 - 312
Main Authors:	Manivel, Laurent, Michałek, Mateusz
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 15-09-2015 Elsevier
Subjects:	Algebraic Geometry Cumulants Generalized determinant Grassmannian Mathematics Minuscule and cominuscule representation Secant variety Grassmannian Generalized determinant 14M15 Minuscule and cominuscule representation Secant variety Cumulants generalized determinant spinor secant variety
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Summary:	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.
ISSN:	0024-3795 1873-1856
DOI:	10.1016/j.laa.2015.04.027