On the existence of minimal models for log canonical pairs

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arxiv 1905.05576 v3 pith:JQA7RH4Q submitted 2019-05-14 math.AG

Vladimir Lazić , Nikolaos Tsakanikas This is my paper · ORCID

classification math.AG

keywords minimalmodelscanonicalexistencepairsassumingexistsmooth

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We show that minimal models of log canonical pairs exist, assuming the existence of minimal models of smooth varieties.

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Abundance for uniruled pairs which are not rationally connected
math.AG 2019-08 accept novelty 8.0 of 10

Assuming the Minimal Model Program in dimension n-1, every uniruled but not rationally connected projective log canonical pair of dimension n with pseudoeffective log canonical divisor has a good model.
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.
The volume function is upper semicontinuous on families of divisors
math.AG 2025-04 conditional novelty 6.0 of 10

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.