Cone theorem and Mori hyperbolicity

Osamu Fujino

Cone theorem and Mori hyperbolicity

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arxiv 2102.11986 v3 pith:4G6RJDAE submitted 2021-02-23 math.AG

Osamu Fujino This is my paper · ORCID

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keywords locusmoriquasi-logconehyperbolicityschemestheoremanswers

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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.

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Discreteness of volumes of divisors on Calabi-Yau type varieties
math.AG 2025-08 conditional novelty 7.0 of 10

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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