  A scheme X \subset \PP^{n} of codimension c is called standard determinantal
if its homogeneous saturated ideal can be generated by the t x t minors of a
homogeneous t x (t+c-1) matrix (f_{ij}). Given integers a_0 \le a_1 \le ...\le
a_{t+c-2} and b_1 \le ...\le b_t, we denote by W_s(b;a) \subset Hilb(\PP^{n})
the stratum of standard determinantal schemes where f_{ij} are homogeneous
polynomials of degrees a_j-b_i and Hilb(\PP^{n}) is the Hilbert scheme (if n-c
> 0, resp. the postulation Hilbert scheme if n-c = 0).
  Focusing mainly on zero and one dimensional determinantal schemes we
determine the codimension of W_s(b;a) in Hilb(\PP^{n}) and we show that
Hilb(\PP^{n}) is generically smooth along W_s(b;a) under certain conditions.
For zero dimensional schemes (only) we find a counterexample to the conjectured
value of dim W_s(b;a) appearing in [26].
