## Current Developments in Mathematics

- Current Developments in Mathematics
- Volume 2007 (2009), 43-76.

### Finite generation of a canonical ring

#### Abstract

The purpose of this note is to review an algebraic proof of the finite generation theorem due to Birkar-Cascini-Hacon-McKernan [5] whose method is based on the Minimal Model Program (MMP). An analytic proof by Siu [57] will be reviewed by Mihai Paun.

#### Article information

**Source**

Current Developments in Mathematics, Volume 2007 (2009), 43-76.

**Dates**

First available in Project Euclid: 5 October 2009

**Permanent link to this document**

https://projecteuclid.org/euclid.cdm/1254748603

**Mathematical Reviews number (MathSciNet)**

MR2532995

**Zentralblatt MATH identifier**

1183.14010

#### Citation

Kawamata, Yujiro. Finite generation of a canonical ring. Current Developments in Mathematics 2007 (2009), 43--76. https://projecteuclid.org/euclid.cdm/1254748603