Uniform bounds for the Iitaka fibration

TL;DR

This paper establishes effective bounds for the uniformity of the Iitaka fibration by deriving an effective birationality theorem for certain adjoint linear series, improving previous results with explicit bounds.

Contribution

It provides the first effective bounds for the uniformity of the Iitaka fibration, based on an effective birationality theorem for adjoint linear series.

Findings

Derived explicit bounds for the Iitaka fibration's uniformity

Established an effective version of the main theorem in [17]

Enhanced understanding of the birationality of adjoint linear series

Abstract

We give effective bounds for the uniformity of the Iitaka fibration. These bounds follow from an effective theorem on the birationality of some adjoint linear series. In particular we derive an effective version of the main theorem in [17].