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Cone theorem and Mori hyperbolicity
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We discuss the cone theorem for quasi-log schemes and the Mori hyperbolicity. In particular, we establish that the log canonical divisor of a Mori hyperbolic projective normal pair is nef if it is nef when restricted to the non-lc locus. This answers Svaldi's question completely. We also treat the uniruledness of the degenerate locus of an extremal contraction morphism for quasi-log schemes. Furthermore, we prove that every fiber of a relative quasi-log Fano scheme is rationally chain connected modulo the non-qlc locus.
Forward citations
Cited by 2 Pith papers
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Discreteness of volumes of divisors on Calabi-Yau type varieties
Volumes of integral divisors on epsilon-lc Calabi-Yau pairs lie in a fixed discrete set, settling Birkar's boundedness conjecture for polarized log Calabi-Yau pairs.
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The volume function is upper semicontinuous on families of divisors
The volume of a divisor on the generic fiber of a flat family equals the infimum of its volumes on any dense family of fibers, yielding upper semicontinuity for reduced irreducible fibers.
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