3 problems

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Sharp cone-length conjecture for log canonical pairs
Sharp cone-length conjecture. It is conjectured that
Conjecturesolvedbirational-geometry cone-theorem log-canonical-pairsarXiv posted 2 days ago
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Conjecture on quasi-log schemes and short affine-line curves
Let $[X,omega]$ be a quasi-log scheme and let $ipi\colon X\to S$ be a projective morphism between schemes such that $-omega$ is $ipi$ -ample and the induced morphism from the non-ql…
Conjectureopencone-theorem quasi-log-schemes rational-curvesarXiv posted 2 days ago
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Cone theorem for generalized log canonical pairs
Cone theorem for g-lc pairs. There are countably many curves $C_j\subset X$ such that $0<-(K_X+B+M)\cdot C_j\leq 2\dim X$ and
Conjectureopencone-theorem generalized-pairs minimal-model-programarXiv posted 2 days ago

Sharp cone-length conjecture for log canonical pairs