Notes on toric varieties from Mori theoretic viewpoint, II

TL;DR

This paper provides improved estimates for extremal rays in toric varieties, explores their implications for adjoint bundles, and generalizes key positivity results like Fujita's theorems.

Contribution

It introduces the best possible estimates for extremal rays of birational type in toric varieties and extends positivity results to broader classes of toric varieties.

Findings

New optimal estimates for extremal rays

Applications to nefness and pseudo-effectivity of adjoint bundles

Generalizations of Fujita's freeness and very ampleness

Abstract

We give new estimates of lengths of extremal rays of birational type for toric varieties. We can see that our new estimates are the best by constructing some examples explicitly. As applications, we discuss the nefness and pseudo-effectivity of adjoint bundles of projective toric varieties. We also treat some generalizations of Fujita's freeness and very ampleness for toric varieties.