On finite generation and boundedness of adjoint foliated structures
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915243522785280 |
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| author | Cascini, Paolo Han, Jingjun Liu, Jihao Meng, Fanjun Spicer, Calum Svaldi, Roberto Xie, Lingyao |
| author_facet | Cascini, Paolo Han, Jingjun Liu, Jihao Meng, Fanjun Spicer, Calum Svaldi, Roberto Xie, Lingyao |
| contents | We prove the existence of good minimal models for any klt algebraically integrable adjoint foliated structure of general type, and that Fano algebraically integrable adjoint foliated structures with total minimal log discrepancies and parameters bounded away from zero form a bounded family. These results serve as the algebraically integrable foliation analogues of the finite generation of the canonical rings proved by Birkar-Cascini-Hacon-M\textsuperscript{c}Kernan, and the Borisov-Alexeev-Borisov conjecture on the boundedness of Fano varieties proved by Birkar, respectively.
As an application, we prove that the ambient variety of any lc Fano algebraically integrable foliation is of Fano type, provided the ambient variety is potentially klt. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_10737 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On finite generation and boundedness of adjoint foliated structures Cascini, Paolo Han, Jingjun Liu, Jihao Meng, Fanjun Spicer, Calum Svaldi, Roberto Xie, Lingyao Algebraic Geometry 14E30, 37F75 We prove the existence of good minimal models for any klt algebraically integrable adjoint foliated structure of general type, and that Fano algebraically integrable adjoint foliated structures with total minimal log discrepancies and parameters bounded away from zero form a bounded family. These results serve as the algebraically integrable foliation analogues of the finite generation of the canonical rings proved by Birkar-Cascini-Hacon-M\textsuperscript{c}Kernan, and the Borisov-Alexeev-Borisov conjecture on the boundedness of Fano varieties proved by Birkar, respectively. As an application, we prove that the ambient variety of any lc Fano algebraically integrable foliation is of Fano type, provided the ambient variety is potentially klt. |
| title | On finite generation and boundedness of adjoint foliated structures |
| topic | Algebraic Geometry 14E30, 37F75 |
| url | https://arxiv.org/abs/2504.10737 |