Let,$H$ be a hyperplane in $\mathbb{P}^{n}, n\geq 3$ and $C =Z(f_1,...,f_r)$ (where $r=n-1$) be an irreducible curve which does not contain $H$. If we have $\deg(f_i)=d_i$, for each $i$,then can we say by Bézout's Theorem that $|H \cap C| \leq d_1...d_r$? (where points are counted with multiplicity).
Can somebody give a reference of this?
Any help from anyone is welcome