my question concerns a very ample line bundle $L$ on a projective k-scheme. It gives a closed immersion
$i:X \rightarrow P^{N-1}_{k}$
to some projective space over k.
It can be viewed as induced by global sections $s_ 1,...,s_N$ of $L$.
Why do people always say that these sections form a basis of $H^{o}(X,L)$? Surely they generate $L$ in the sense of: generating in every stalk. But why is $N=dim(H^{o}(X,L)$?
Thanks a lot!