Proves Shokurov's global index conjecture for foliations on varieties of dimension at most three.
Positivity of the moduli part
7 Pith papers cite this work. Polarity classification is still indexing.
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Under LMMP and log resolution assumptions in dimension n, the moduli part is nef up to birational map for dlt pairs with f-nef K_X + B over perfect fields of char p>2; unconditional in dimension 3 for p>5.
Introduces K-stability and Ding stability for adjoint foliated structures, proves reduction to special test configurations and valuative criteria via mixed invariants, and shows boundedness of K-semistable adjoint Fano foliated structures with bounded volume.
The optimal constant in the bend-and-break inequality for foliations of rank r on normal projective varieties is r+1.
Algebraically integrable foliations of fixed dimension and bounded adjoint volume are log birationally bounded, which implies birational boundedness for stable families of maximal variation.
The normalization of the moduli space of polarized klt good minimal models of arbitrary Kodaira dimension is quasi-projective.
The paper reviews progress on the minimal model program for foliations, including singularities, adjunction, MMP on surfaces, and flips on threefolds.
citing papers explorer
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Shokurov's global index conjecture for threefold foliations
Proves Shokurov's global index conjecture for foliations on varieties of dimension at most three.
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On the canonical bundle formula in positive characteristic
Under LMMP and log resolution assumptions in dimension n, the moduli part is nef up to birational map for dlt pairs with f-nef K_X + B over perfect fields of char p>2; unconditional in dimension 3 for p>5.
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K-stability of adjoint foliated structures
Introduces K-stability and Ding stability for adjoint foliated structures, proves reduction to special test configurations and valuative criteria via mixed invariants, and shows boundedness of K-semistable adjoint Fano foliated structures with bounded volume.
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Optimal bend-and-break for foliations
The optimal constant in the bend-and-break inequality for foliations of rank r on normal projective varieties is r+1.
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Birational boundedness of stable families
Algebraically integrable foliations of fixed dimension and bounded adjoint volume are log birationally bounded, which implies birational boundedness for stable families of maximal variation.
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Quasi-Projective Moduli for Polarized klt Good Minimal Models
The normalization of the moduli space of polarized klt good minimal models of arbitrary Kodaira dimension is quasi-projective.
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Recent progress on the Minimal Model Program for foliations
The paper reviews progress on the minimal model program for foliations, including singularities, adjunction, MMP on surfaces, and flips on threefolds.