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arXiv · 0903.0679

Nef and big divisors on toric weak Fano 3-folds

Shoetsu Ogata
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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.

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Shoetsu Ogata. 2009-03-04. Nef and big divisors on toric weak Fano 3-folds. https://arxiv.org/abs/0903.0679

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