On the equivalence between the effective adjunction conjectures of Prokhorov-Shokurov and of Li
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| Format: | Preprint |
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2023
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| _version_ | 1866915496187658240 |
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| author | Han, Jingjun Liu, Jihao Xue, Qingyuan |
| author_facet | Han, Jingjun Liu, Jihao Xue, Qingyuan |
| contents | Prokhorov and Shokurov introduced the famous effective adjunction conjecture, also known as the effective base-point-freeness conjecture. This conjecture asserts that the moduli component of an lc-trivial fibration is effectively base-point-free. Li proposed a variation of this conjecture, which is known as the $Γ$-effective adjunction conjecture, and proved that a weaker version of his conjecture is implied by the original Prokhorov-Shokurov conjecture.
In this paper, we establish the equivalence of Prokhorov-Shokurov's and Li's effective adjunction conjectures. The key to our proof is the formulation of a uniform rational polytope for canonical bundle formulas, which relies on recent developments in the minimal model program theory of algebraically integrable foliations by Ambro-Cascini-Shokurov-Spicer and Chen-Han-Liu-Xie. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_15397 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the equivalence between the effective adjunction conjectures of Prokhorov-Shokurov and of Li Han, Jingjun Liu, Jihao Xue, Qingyuan Algebraic Geometry Dynamical Systems 14E30, 37F75 Prokhorov and Shokurov introduced the famous effective adjunction conjecture, also known as the effective base-point-freeness conjecture. This conjecture asserts that the moduli component of an lc-trivial fibration is effectively base-point-free. Li proposed a variation of this conjecture, which is known as the $Γ$-effective adjunction conjecture, and proved that a weaker version of his conjecture is implied by the original Prokhorov-Shokurov conjecture. In this paper, we establish the equivalence of Prokhorov-Shokurov's and Li's effective adjunction conjectures. The key to our proof is the formulation of a uniform rational polytope for canonical bundle formulas, which relies on recent developments in the minimal model program theory of algebraically integrable foliations by Ambro-Cascini-Shokurov-Spicer and Chen-Han-Liu-Xie. |
| title | On the equivalence between the effective adjunction conjectures of Prokhorov-Shokurov and of Li |
| topic | Algebraic Geometry Dynamical Systems 14E30, 37F75 |
| url | https://arxiv.org/abs/2312.15397 |