Nef and big divisors on toric weak Fano 3-folds

2009/03/04 by Ogata, Shoetsu
#14M25 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0903.0679

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 all ample line bundles on a nonsingular toric weak Fano 3-fold are normally generated. We also show that an ample line bundle whose adjoint bundle has non-zero global sections on a Gorensein toric Fano 3-fold is normally generated. In our proof we do not use full classifications of Fano polytopes.

Related

• Exceptional Collections of Line Bundles for Smooth Toric Fano Surfaces and Threefolds
• The classification of smooth toric weakened Fano 3-folds
• Threefolds of globally F-regular type with nef anti-canonical divisor
• Smooth projective toric varieties whose nontrivial nef line bundles are big
• Images of toric variety and amplified endomorphism of weak Fano threefolds