Sets of singular restrictions of symplectic forms

Abstract

Let $Ω$ be a non-singular syplectic form on some vector space $V$. Denote by $S^{n}_{k}(Ω)$ the set of all $k$-dimensional planes $s$ in $V$ such that the restriction of $Ω$ onto $s$ is singular. For the cases when $k=2,n-2$ a simple geometric characteristic of $S^{n}_{k}(Ω)$ will be described.