On \(d\)-spannedness of the adjoint bundles on polarized manifolds
Fix \(L\in\text{Pic}(X)\) a with \(X\) a smooth \(n\)-dimensional projective variety. \(L\) is said \(d\)-spanned \((d\geq 0)\) if for every curvilinear 0-dimensional subscheme \(Z\) of \(X\) with \(\text{length} (Z)\leq d+1\) the restriction map \(H^0(X,L)\to H^0(Z,L| Z)\) is surjective. Here the author gives for all integers \(n,d\) a nice example of a pair \((X,L)\) as above with \(L\) ample and \(d\)-spanned but for which \(K_X+ (n+d)L\) is not \(d\)-spanned.
scientific article; zbMATH DE number 1269767