On the pluricanonical maps of varieties of intermediate Kodaira dimension

TL;DR

This paper proves a uniformity result for the Iitaka fibration of varieties with intermediate Kodaira dimension, under certain conditions on the fibers and variation, advancing understanding of pluricanonical maps.

Contribution

It establishes a new uniformity result for pluricanonical maps of varieties with intermediate Kodaira dimension, especially when the generic fiber has a good minimal model or the variation is zero.

Findings

Proves a uniformity result for the Iitaka fibration under specific conditions.

Shows the result holds when the generic fiber has a good minimal model.

Demonstrates the case when the variation of the fibration is zero.

Abstract

In this paper we will prove a uniformity result for the Iitaka fibration $f:X \rightarrow Y$, provided that the generic fiber has a good minimal model and the variation of $f$ is zero or that $\kappa(X)=\rm{dim}(X)-1$.