On the Minimal Model Program for K\"ahler 3-folds

TL;DR

This paper advances the minimal model program for compact K"ahler 3-folds by establishing key contraction and flip existence results, assuming lower-dimensional cases, and provides a comprehensive proof of foundational theorems in dimension 3.

Contribution

It proves the existence of pl-flips and contractions in higher dimensions assuming lower-dimensional MMP results, and offers a self-contained proof of core theorems in dimension 3.

Findings

Existence of pl-flipping and divisorial contractions in dimension n

Self-contained proof of the cone theorem in dimension 3

Establishment of flips and minimal models in dimension 3

Abstract

In this article we prove the existence of pl-flipping and divisorial contractions and pl flips in dimension $n$ for compact K\"ahler varieties, assuming results of the minimal model program in dimension $n-1$. We also give a self contained proof of the cone theorem, the existence of flipping and divisorial contractions, of flips and minimal models in dimension 3.