Secants of minuscule and cominuscule minimal orbits

Mateusz Michalek Michalek (1) , Laurent Manivel (2)

1 IF - Institut Fourier
2 I2M - Institut de Mathématiques de Marseille

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.

Mots clés: secant variety; Grassmannian; spinor; generalized determinant

Domaines: Géométrie algébrique [math.AG]

Mateusz Michalek Michalek, Laurent Manivel. Secants of minuscule and cominuscule minimal orbits. Linear Algebra and its Applications, 2015, 481, pp.288-312. ⟨10.1016/j.laa.2015.04.027⟩. ⟨hal-01265416⟩