Existence of Good Minimal Models for K\"ahler Varieites of Maximal Albanese Dimension

TL;DR

This paper proves that compact K"ahler klt pairs with maximal Albanese dimension always admit good minimal models, meaning their canonical divisors become semi-ample after a suitable bimeromorphic contraction.

Contribution

It establishes the existence of good minimal models for a new class of K"ahler varieties with maximal Albanese dimension, extending minimal model theory.

Findings

Existence of good minimal models for K"ahler klt pairs of maximal Albanese dimension.

Semi-ampleness of the canonical divisor after bimeromorphic contraction.

Extension of minimal model theory to certain K"ahler varieties.

Abstract

In this short article we show that if $(X, B)$ is a compact K\"ahler klt pair of maximal Albanese dimension, then it has a good minimal model, i.e. there is a bimeromorphic contraction $\phi:X\dashrightarrow X'$ such that $K_{X'}+B'$ is semi-ample.