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On finite generation and boundedness of adjoint foliated structures
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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.
Forward citations
Cited by 2 Pith papers
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Sarkisov program for algebraically integrable and threefold foliations
The authors establish that for algebraically integrable foliations on klt varieties, and for rank one foliations on threefolds, any two Mori fiber spaces are connected by Sarkisov links.
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$\Theta$-reductivity and $S$-completeness for adjoint Fano foliated structures
Theta-reductivity and S-completeness hold for the moduli problem of t-K-semistable adjoint Fano foliated structures, yielding uniqueness of K-polystable degenerations and reductivity of automorphism groups.
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