Variation of algebraically integrable adjoint foliated structures
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916986945011712 |
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| author | Cascini, Paolo Liu, Jihao Meng, Fanjun Svaldi, Roberto Xie, Lingyao |
| author_facet | Cascini, Paolo Liu, Jihao Meng, Fanjun Svaldi, Roberto Xie, Lingyao |
| contents | Given a canonical algebraically integrable foliation on a klt projective variety, we study the variation of the ample models of the associated adjoint foliated structures with respect to the parameter. When the foliation is of general type, we show the finiteness of ample models if the parameter is sufficiently close to $1$. When the ambient variety is of general type, we show the finiteness of ample models for all parameters. A key ingredient in our proof is the equivalence between the existence of minimal models and the termination of MMP with scaling for algebraically integrable adjoint foliated structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_02498 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Variation of algebraically integrable adjoint foliated structures Cascini, Paolo Liu, Jihao Meng, Fanjun Svaldi, Roberto Xie, Lingyao Algebraic Geometry Dynamical Systems 14E30, 37F75 Given a canonical algebraically integrable foliation on a klt projective variety, we study the variation of the ample models of the associated adjoint foliated structures with respect to the parameter. When the foliation is of general type, we show the finiteness of ample models if the parameter is sufficiently close to $1$. When the ambient variety is of general type, we show the finiteness of ample models for all parameters. A key ingredient in our proof is the equivalence between the existence of minimal models and the termination of MMP with scaling for algebraically integrable adjoint foliated structures. |
| title | Variation of algebraically integrable adjoint foliated structures |
| topic | Algebraic Geometry Dynamical Systems 14E30, 37F75 |
| url | https://arxiv.org/abs/2510.02498 |