Let, $X$ be a zero dimensional subscheme of $\Bbb P^n$ and let us define a function as follows:

$h_{\Bbb P^n}(X ,d) = \binom {n+d}{n}$ - dim $I_{X}(d)$ , where dim $I_{X}(d)$ = the dimension of vector space of all homogeneous polynomial of degree $d$ which passes through $X$.

Is it true that the function defined above is semicontinuous?

If it's so then how one proves it? Can someone give references on this?