Uniform rational polytopes for Iitaka dimensions

TL;DR

This paper advances the theory of Iitaka dimensions by establishing uniform perturbations and the existence of rational polytopes for pseudo-effective lc pairs, contingent on the non-vanishing conjecture.

Contribution

It introduces the concept of uniform rational polytopes for Iitaka dimensions and demonstrates their existence under certain conjectural assumptions.

Findings

Existence of uniform rational polytopes for Iitaka dimensions.

Uniform perturbation results for Iitaka dimensions.

Results depend on the non-vanishing conjecture.

Abstract

In this paper, we continue to develop the theories on functional pairs and uniform rational polytopes. We show that there is a uniform perturbation for Iitaka dimensions of pseudo-effective lc pairs of fixed dimension with DCC coefficients assuming the non-vanishing conjecture. We also show the existence of uniform rational polytopes for Iitaka dimensions of pseudo-effective lc pairs assuming the non-vanishing conjecture.