On the Generation of Certain Bundles of the Projective Space

Extending a result of Manivel, we prove the following: THEOREM. Suppose ∑_ib_i ≥ ∑_ja_j+n and ∑_ib_i [n+d_id_i −1] ≥ ∑_ja_j [n+l_jl_j −1] +n. Then the kernel E(d) of the general morphism: ⊕^v_i=1 (B_i ⊗ O_pⁿ (d_i))→⊕^v_j=1(A_j ⊗ O_pⁿ (l_j)) (l₁ … >l_s > d₁ …>d_v) is a globally generated vector bundle, except for at most finitely many sets { b_i, a_j}.