Boundedness of log Calabi-Yau pairs of Fano type

TL;DR

This paper proves a boundedness result for certain log Calabi-Yau pairs of Fano type, leading to progress on the Effective Iitaka Fibration Conjecture for pairs with big boundary.

Contribution

It establishes a boundedness result for klt pairs with numerically trivial canonical class and big boundary, advancing the understanding of their classification.

Findings

Boundedness of klt pairs with $K_X+B\equiv 0$ and big $B$.

Positive resolution of the Effective Iitaka Fibration Conjecture for such pairs.

Abstract

We prove a boundedness result for klt pairs $(X,B)$ such that $K_X+B\equiv 0$ and $B$ is big. As a consequence we obtain a positive answer to the Effective Iitaka Fibration Conjecture for klt pairs with big boundary.