Nef and big divisors on toric weak Fano 3-folds

Abstract

We show that a nef and big line bundle whose adjoint bundle has non-zero global sections on a nonsingular toric weak Fano 3-fold is normally generated. As a consequence, we see that any ample line bundle on a nonsingular toric waek Fano 3-fold is normally generated. As an application, we see that an ample line bundle on a Calabi-Yau hypersurface in a nonsingular toric Fano 4-fold is normally generated. Mathematics Subject Classification: Primary 14M25; Secondary 14M30, 14M45, 52B20