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Log abundance of the moduli b-divisors of lc-trivial fibrations
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abstract
We prove that the moduli b-divisor of an lc-trivial fibration from a log canonical pair is log abundant. The result follows from a theorem on the restriction of the moduli b-divisor, based on a theory of lc-trivial morphisms, which allows us to treat $\mathbb{R}$-divisors and proper morphisms possibly with disconnected fibres. We also prove a theorem on extending a finite cover over a closed subvariety to that over a variety in arbitrary characteristic.
Forward citations
Cited by 3 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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$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs
A P-trivial MMP is introduced and used to show that several classes of generalised klt and lc pairs with Nakayama-Zariski decompositions have minimal models.
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Minimal model program for normal pairs along log canonical locus in complex analytic setting
The complex analytic analog of the minimal model program for normal pairs along the log canonical locus holds: under a semi-ampleness hypothesis on the non-lc locus, an MMP sequence exists and terminates at a good min...
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