Secants of minuscule and cominuscule minimal orbits
arXiv:1401.1956 · doi:10.1016/j.laa.2015.04.027
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.
References in corpus (2)
Cited by in corpus (13)
- Plethysm and lattice point counting
- Ideals of bounded rank symmetric tensors are generated in bounded degree
- Syzygies of bounded rank symmetric tensors are generated in bounded degree
- Permanent versus determinant: not via saturations
- Plücker varieties and higher secants of Sato's Grassmannian
- Identifiability and singular locus of secant varieties to Grassmannians
- Symmetrization of Principal Minors and Cycle-Sums
- Plethysm and fast matrix multiplication
- Lagrangian Grassmannians and Spinor Varieties in Characteristic Two
- Cotangent Bundle to the Flag Variety - I
- Identifiability and singular locus of secant varieties to spinor varieties
- Collineation varieties of tensors
- Flexible affine cones and flexible coverings