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Invariance of Plurigenera and boundedness for Generalized Pairs

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arxiv 2005.04254 v3 pith:PYVV4DT4 submitted 2020-05-08 math.AG

Stefano Filipazzi , Roberto Svaldi This is my paper · ORCID
classification math.AG
keywords boundednessgeneralizedpairsinvarianceplurigenerasomevarietiesalgebraic
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abstract

In this note, we survey some recent developments in birational geometry concerning the boundedness of algebraic varieties. We delineate a strategy to extend some of these results to the case of generalized pairs, first introduced by Birkar and Zhang, when the associated log canonical divisor is ample, and the volume is fixed. In this context, we show a version of deformation invariance of plurigenera for generalized pairs. We conclude by discussing an application to the boundedness of varieties of Kodaira dimension $\kappa(X)=\dim(X)-1$.

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  1. 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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