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Log canonical $3$-fold complements

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arxiv 1909.10098 v2 pith:WMTZ73LB submitted 2019-09-22 math.AG

Stefano Filipazzi , Joaquín Moraga , Yanning Xu This is my paper · ORCID
classification math.AG
keywords calabi-yaucanonicalfoldcomplementstypecontractiondimensionaleffective
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abstract

We expand the theory of log canonical $3$-fold complements. We prove that if $X\rightarrow T$ is a $3$-dimensional contraction of log Calabi-Yau type, then we can find $B\geq 0$ on $X$ for which $(X,B)$ is log canonical and $n(K_X+B)\sim_T 0$, where $n$ is an uniform natural number. This means that every $3$-fold of log Calabi-Yau type can be turned into a log Calabi-Yau pair in an effective way.

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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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