Let $L_1, ..., L_n$ be non-intersecting (general, if necessary) lines in $\mathbb P^3$. I need to find the dimension of the space of polynomials of degree $d$, vanishing on these lines.
Cohomologically speaking, its $h_0(\mathbb P^3, I_{\bigsqcup L_i}(d)$. Unfortjnately, the exact sequence $0 \to I_{\bigsqcup L_i}(d) \to \mathcal O_{\mathbb P^3}(d) \to \mathcal O_{\bigsqcup L_i}(d) \to 0$ does not help.