Non-vanishing theorem for generalized log canonical pairs with a polarization

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arxiv 2012.15038 v1 pith:EJCF2SA5 submitted 2020-12-30 math.AG

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We prove that the non-vanishing conjecture holds for generalized lc pairs with a polarization.

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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.