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.
Generalised pairs in birational geometry
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abstract
In this note we introduce generalised pairs from the perspective of the evolution of the notion of space in birational algebraic geometry. We describe some applications of generalised pairs in recent years and then mention a few open problems.
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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.