Spreads of nonsingular pairs in symplectic vector spaces

Abstract.

Let V be a vector space of dimension 2n, n even, over a field F, equipped with a nonsingular symplectic form. We define a new algebraic/combinatorial structure, a spread of nonsingular pairs, or nsp-spread, on V and show that nsp-spreads exist in considerable generality. We further examine in detail some particular cases.