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.
Secants of Lagrangian Grassmannians / Boralevi, Ada; J., Buczynski. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - 190:4(2011), pp. 725-739. [10.1007/s10231-010-0171-0]
Secants of Lagrangian Grassmannians
Boralevi, Ada;
2011-01-01
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.File in questo prodotto:
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