ON THE DIMENSION OF THE GLOBAL SECTIONS OF THE ADJOINT BUNDLE FOR POLARIZED 5-FOLDS

Abstract

Let (X, L) denote a polarized manifold of dimension five. This study considers the dimension of the global sections of K_X + mL with m ≥ 6. In particular, we prove that h⁰(K_X + mL) ≥ (^m−1₅) for any polarized 5-fold (X, L) with h⁰(L) > 0. Furthermore, we also consider (X, L) with h⁰ (K_X + mL) = (^m−1₅) for some m ≥ 6 with h⁰(L) > 0.