On minimum size blocking sets of external lines to a quadric in PG(d,q)

We characterize the minimum size blocking sets with respect to the external lines to a non-singular quadric or a quadric with a point vertex in PG($d,q$), $d\ge 4$ and $q\ge 9$. Our results show that these minimum size blocking sets are equal to the sets of points not on the quadric in a suitably chosen hyperplane with respect to the quadric.