On Effective Iitaka Fibration Indices for Stable Minimal Models with Large Iitaka Volumes

TL;DR

This paper investigates conditions under which certain linear systems induce Iitaka fibrations on stable minimal models with large Iitaka volumes, focusing on effective indices.

Contribution

It provides criteria for when the linear system |m(K_V+C)| induces an Iitaka fibration in the context of stable minimal models with large Iitaka volumes.

Findings

Identifies bounds on m for inducing Iitaka fibrations

Establishes relations between Iitaka volume and fibration induction

Provides new insights into stable minimal models with fixed coefficients

Abstract

Given a pair $(V,C)$ that admits a stable minimal model with fixed dimension, fixed coefficient set, and bounded relative volume, we study when the linear system $|m(K_V+C)|$ induces an Iitaka fibration, assuming the Iitaka volume of $K_V+C$ is sufficiently large.