On termination of log flips in dimension four

TL;DR

This paper proves that in four-dimensional algebraic geometry, certain types of transformations called log flips always conclude when dealing with klt pairs of Kodaira dimension at least 2, advancing the understanding of the minimal model program.

Contribution

It establishes the termination of 4-fold log flips specifically for klt pairs with Kodaira dimension ≥ 2, filling a gap in the minimal model program.

Findings

Termination of 4-fold log flips proven for klt pairs with κ ≥ 2

Advances the minimal model program in higher dimensions

Provides new techniques for analyzing log flips in dimension four

Abstract

We prove the termination of 4-fold log flips for klt pairs of Kodaira dimension $\kappa\ge 2$.