2 problems

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Tian's strong stabilization conjecture for alpha-invariants
Tian's strong stabilization conjecture. If $R(X,L)$ is generated by
Conjecturerefutedfano-varieties log-canonical-thresholds section-ringsarXiv posted 2 days ago
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Kawamata's adjoint-ideal conjecture for Gorenstein section rings
Kawamata's conjecture in the Fano case. One has
Conjectureopencommutative-algebra multiplier-ideals section-ringsarXiv posted 2 days ago

Tian's strong stabilization conjecture for alpha-invariants