$\begingroup$
This is an exercise in Vakil's FOAG,page 711
I don't know how to use the Cohomology and Base Change Theorem,becasue if we want to use the theorem,we need to show that the base change morphism $\phi_q^0:pr_1{_*}(\mathscr L )\otimes k(q)\to H^0(X\times\mathbb P^n|_q,\mathscr L|_{X\times\mathbb P^n|_q})$ is surjective for every point $q$ in $X$,which in this situation means that there is a section of $\mathscr L$ over $\mathbb P^n_A$ not vanish over the fiber of $q$ for some affine open subset $Spec A$ around $q$,which is not clear to me.
$\endgroup$ 3 Reset to default
