Sets of generators blocking all generators in finite classical polar spaces

We introduce generator blocking sets of finite classical polar spaces. These sets are a generalisation of maximal partial spreads. We prove a characterization of these minimal sets of the polar spaces Q ( 2 n , q ) , Q − ( 2 n + 1 , q ) and H ( 2 n , q 2 ) , in terms of cones with vertex a subspace contained in the polar space and with base a generator blocking set in a polar space of rank 2.