On finite generation and boundedness of adjoint foliated structures

2025/04/14 by Paolo Cascini, Cascini, Paolo, Jingjun Han +11 · 5 citations
Mathematics · #Geometry and complex manifolds #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.2504.10737

Abstract

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\textsuperscriptcKernan, 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.

Cited by

• Volumes of foliations birationally bounded by algebraically integrable families
• Variation of algebraically integrable adjoint foliated structures
• Non-algebraicity of non-abundant foliations and abundance for adjoint foliated structures
• MMP for generalized foliated threefolds of rank one
• Sarkisov program for algebraically integrable and threefold foliations

Related

• Variation of algebraically integrable adjoint foliated structures
• Minimal model program for algebraically integrable adjoint foliated structures
• Minimal model program for algebraically integrable foliations on klt varieties
• Existence of complements for foliations
• Non-algebraicity of non-abundant foliations and abundance for adjoint foliated structures