Ample line bundles on certain toric fibered 3-folds

TL;DR

This paper proves that on certain smooth toric 3-folds with a fibration over the projective line, every ample line bundle is normally generated, contributing to the understanding of line bundle properties in toric geometry.

Contribution

It establishes that ample line bundles on specific toric fibered 3-folds are always normally generated, a new result in the study of line bundles on toric varieties.

Findings

Ample line bundles on these toric 3-folds are normally generated.

The result applies to projective nonsingular toric 3-folds with a torus equivariant morphism to P^1.

The theorem enhances understanding of line bundle properties in toric fibered varieties.

Abstract

Let $X$ be a projective nonsingular toric 3-fold with a surjective torus equivariant morphism onto the projective line. Then we prove that an ample line bundle on $X$ is always normally generated.