MMP for Generalized Pairs on K\"ahler 3-folds

Author:

Omprokash Das, Christopher Hacon, José Ignacio Yáñez

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Complex Variables (math.CV)

journal:

date:

2023-04-29 16:00:00

Abstract

In this article we define generalized pairs $(X, B+\boldsymbol{\beta})$ where $X$ is an analytic variety and $\boldsymbol{\beta}$ is a b-(1,1) current. We then prove that almost all standard results of the MMP hold in this generality for compact K\"ahler varieties of dim $X\leq 3$. More specifically, we prove the cone theorem, existence of flips, existence of log terminal models, log canonical models and Mori fiber spaces, the geography of log canonical and log terminal models, etc.

PDF: MMP for Generalized Pairs on K\"ahler 3-folds.pdf