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Positivity of the Moduli Part
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We prove the Cone Theorem for algebraically integrable foliations. As a consequence, we show that termination of flips implies the b-nefness of the moduli part of a log canonical pair with respect to a contraction, generalising the case of lc trivial fibrations.
Forward citations
Cited by 5 Pith papers
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Boundedness of some fibered K-trivial varieties
Fixed-dimension Calabi-Yau varieties with abelian or primitive symplectic fibrations are birationally bounded, and Lagrangian-fibered primitive symplectic varieties have finitely many deformation classes.
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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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Effective positivity of Hodge bundles and applications
The paper proves effective positivity of Hodge bundles for stable families and derives uniform lower bounds on volumes and automorphism groups, in terms only of dimension and allowed boundary coefficients.
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On the boundedness of elliptic Calabi-Yau 4-folds
Elliptic Calabi–Yau 4-folds not crepant to a product quotient of a Calabi–Yau 3-fold times an elliptic curve form a bounded family.
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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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