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?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.