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arXiv · 2502.00790

On minimal model program and Zariski decomposition of potential triples

Sung Rak Choi·Sungwook Jang·Dae-Won Lee
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Abstract

In this paper, we investigate properties of potential triples $(X,\Delta,D)$ which consists of a pair $(X,\Delta)$ and a pseudoeffective $\mathbb{R}$-Cartier divisor $D$. In particular, we show that if $D$ admits a birational Zariski decomposition, then one can associate a generalized pair structure to the potential triple $(X,\Delta,D)$. Moreover, we can run the generalized MMP on $(K_X+\Delta+D)$ as special cases. As an application, we also show that for a pklt pair $(X,\Delta)$, if $-(K_X+\Delta)$ admits a birational Zariski decomposition with $\mathrm{NQC}$ positive part, then there exists a $-(K_X+\Delta)$-minimal model.

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Sung Rak Choi, Sungwook Jang, Dae-Won Lee. 2025-02-02. On minimal model program and Zariski decomposition of potential triples. https://arxiv.org/abs/2502.00790

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