New outlook on the Minimal Model Program, II

TL;DR

This paper demonstrates that the finite generation of adjoint rings, established in prior work, underpins all key foundational results of the Minimal Model Program, streamlining the understanding of its core theorems.

Contribution

It shows that finite generation results imply the main theorems of the Minimal Model Program, unifying foundational aspects under a single framework.

Findings

Finite generation of adjoint rings implies the Rationality, Cone, and Contraction theorems.

It establishes the existence of flips and their termination with scaling.

Provides a new perspective linking finite generation to core MMP results.

Abstract

We prove that the finite generation of adjoint rings proved in [Cascini and Lazi\'c] implies all the foundational results of the Minimal Model Program: the Rationality, Cone and Contraction theorems, the existence of flips, and termination of flips with scaling in the presence of a big boundary.