Proves existence of numerically good minimal models for generalized klt pairs of relative log numerical dimension zero assuming Generalized Nonvanishing via a numerical generalized canonical bundle formula.
MMP for Generalized Pairs on K\"ahler 3-folds
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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.
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math.AG 1years
2026 1verdicts
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On the minimal model theory for generalized pairs of relative log numerical dimension zero
Proves existence of numerically good minimal models for generalized klt pairs of relative log numerical dimension zero assuming Generalized Nonvanishing via a numerical generalized canonical bundle formula.