New outlook on the Minimal Model Program, I

TL;DR

This paper presents a new proof for the finite generation of adjoint rings with big boundaries, leading to the conclusion that the canonical ring of a smooth projective variety is finitely generated.

Contribution

It provides a new, self-contained proof of finite generation results in the Minimal Model Program, specifically for adjoint rings and canonical rings.

Findings

Finite generation of adjoint rings with big boundaries.

Canonical ring of a smooth projective variety is finitely generated.

New proof simplifies understanding of the Minimal Model Program.

Abstract

We give a new and self-contained proof of the finite generation of adjoint rings with big boundaries. As a consequence, we show that the canonical ring of a smooth projective variety is finitely generated.