Boundedness of threefolds of Fano type with Mori fibration structures

TL;DR

This paper proves that three-dimensional varieties of Fano type with Mori fibrations are bounded, using previous birational boundedness results and classical arguments, advancing the classification of algebraic threefolds.

Contribution

It establishes the boundedness of 3-folds of epsilon-Fano type with Mori fibrations, combining prior birational boundedness results with classical techniques.

Findings

Boundedness of 3-folds of epsilon-Fano type with Mori fibrations.

Extension of previous birational boundedness results.

Application of classical arguments in the proof.

Abstract

We show boundedness of $3$-folds of $\epsilon$-Fano type with Mori fibration structures. The proof is based on the birational boundedness result in our previous work arXiv:1509.08722 combining with arguments in Kawamata \cite{K} and Koll\'ar--Miyaoka--Mori--Takagi \cite{KMMT}.