Thanks. Is it true for Stein manifolds? I mean, by Hormander's theorem, the global sections generate the vector bundle. So, if the global sections are finite dimensional it ought to be true, ought not it?

For some reason I can't seem to edit it.

Thanks. The description in terms of matrices was concrete indeed But, how does one describe the hilbert scheme of X where X is a general complex 2-manifold? I mean, in Gottsche's slides (for a talk) it is written that atleast as a set it is the collection {(x1,Q1),(x2,Q2),....(xk,Qk)} where where xk is a point on X and Qk is "the quotient ring of holomorphic functions at xk" (any idea as to what this means?).