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Let $(X, A)$ be a nonsingular polarized toric 3-fold. We show that if theadjoint bundle of $A$ has no glabal section, then all ample line bundles on $X$are normally generated. Even if the adjoint bundle is effective, if it is notbig, then it is shown the normal generation. In particular, we show that allample line bundles on a nonsingular toric Fano 3-fold are normally generated.

Projective normality of toric 3-folds with non-big adjoint hyperplane sections, II