PROJECTIVE NORMALITY OF TORIC 3-FOLDS WITH NON-BIG ADJOINT HYPERPLANE SECTIONS

Abstract

Let $L$ be an ample line bundle on a nonsingular toric 3-fold. We show that if the adjoint bundle of $L$ has no global sections, then $L$ is normally generated. Even if the adjoint bundle is effective, it is shown that $L$ is normally generated if it is not big.