  In the Hilbert scheme of points on a scheme X there is an open subset
parameterizing distinct points. The closure of that open set is by definition
the good component. When X is flat over the base, we show that a certain
blow-up of the symmetric product of X is the good component. The center of the
blow-up we describe by giving generators for its defining ideal. In the
non-flat case we obtain similar result by replacing the symmetric product with
the divided power product. For smooth surfaces X the good component equals the
Hilbert scheme of points.
