Introduction to the Minimal Model Program and the existence of flips

TL;DR

This paper provides a comprehensive introduction to the Minimal Model Program, detailing key theorems of Mori theory with modern techniques, and offers a detailed proof of flip existence assuming the program with scaling.

Contribution

It presents a complete, self-contained exposition of Mori theory's fundamental theorems and a detailed proof of flip existence assuming the minimal model program with scaling.

Findings

Complete presentation of Mori theory theorems using modern methods

Detailed proof of flip existence in dimension n assuming MMP with scaling

Clarification of the minimal model program's foundational steps

Abstract

The first aim of this note is to give a concise, but complete and self-contained, presentation of the fundamental theorems of Mori theory - the nonvanishing, base point free, rationality and cone theorems - using modern methods of multiplier ideals, Nadel vanishing, and the subadjunction theorem of Kawamata. The second aim is to write up a complete, detailed proof of existence of flips in dimension n assuming the minimal model program with scaling in dimension n-1.