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- W4288022655 abstract "We study the convergence of volume forms on a degenerating holomorphic family of log-Calabi-Yau varieties to a non-Archimedean measure, extending a result of Boucksom and Jonsson. More precisely, let $(X,B)$ be a holomorphic family of sub log canonical, log-Calabi-Yau complex varieties parameterized by the punctured unit disk. Let $eta$ be a meromorphic volume form on $X$ with poles along $B$. We show that the (possibly infinite) measures induced by the restriction of the $eta$ to a fiber converge to a measure on the Berkovich analytification as we approach the puncture. The convergence takes place on a hybrid space, which is obtained by filling in the space $X setminus B$ with the aforementioned Berkovich space over the puncture." @default.
- W4288022655 created "2022-07-26" @default.
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- W4288022655 date "2019-11-17" @default.
- W4288022655 modified "2023-10-17" @default.
- W4288022655 title "Convergence of volume forms on a family of log-Calabi-Yau varieties to a non-Archimedean measure" @default.
- W4288022655 doi "https://doi.org/10.48550/arxiv.1911.07307" @default.
- W4288022655 hasPublicationYear "2019" @default.
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