On minimal model program and Zariski decomposition of potential triples
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913675396251648 |
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| author | Choi, Sung Rak Jang, Sungwook Lee, Dae-Won |
| author_facet | Choi, Sung Rak Jang, Sungwook Lee, Dae-Won |
| contents | In this paper, we investigate properties of potential triples $(X,Δ,D)$ which consists of a pair $(X,Δ)$ 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 $(X,Δ,D)$. Moreover, we can run the generalized MMP on $(K_X+Δ+D)$ as special cases. As an application, we also show that for a pklt pair $(X,Δ)$, if $-(K_X+Δ)$ admits a birational Zariski decomposition with $\mathrm{NQC}$ positive part, then there exists a $-(K_X+Δ)$-minimal model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_00790 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On minimal model program and Zariski decomposition of potential triples Choi, Sung Rak Jang, Sungwook Lee, Dae-Won Algebraic Geometry In this paper, we investigate properties of potential triples $(X,Δ,D)$ which consists of a pair $(X,Δ)$ 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 $(X,Δ,D)$. Moreover, we can run the generalized MMP on $(K_X+Δ+D)$ as special cases. As an application, we also show that for a pklt pair $(X,Δ)$, if $-(K_X+Δ)$ admits a birational Zariski decomposition with $\mathrm{NQC}$ positive part, then there exists a $-(K_X+Δ)$-minimal model. |
| title | On minimal model program and Zariski decomposition of potential triples |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2502.00790 |