Existence of minimal models for varieties of log general type

TL;DR

This paper proves that for smooth projective varieties of log general type, the canonical ring is finitely generated, establishing a key step in the minimal model program.

Contribution

It demonstrates the existence of minimal models for varieties of log general type by proving finite generation of the canonical ring.

Findings

Canonical ring of smooth projective varieties is finitely generated

Supports the existence of minimal models in algebraic geometry

Advances the minimal model program for varieties of log general type

Abstract

We prove that the canonical ring of a smooth projective variety is finitely generated.