Secants of Lagrangian Grassmannians
arXiv:1006.1925 · doi:10.1007/s10231-010-0171-0
Abstract
We study the dimensions of secant varieties of the Grassmannian of Lagrangian subspaces in a symplectic vector space. We calculate these dimensions for third and fourth secant varieties. Our result is obtained by providing a normal form for four general points on such a Grassmannian and by explicitly calculating the tangent spaces at these four points.