Semi-stable Extensions Over 1-dimensional Bases

Given a family of Calabi-Yau varieties over the punctured disc or over the field of Laurentseries, we show that, after a finite base change, the family can be extended across the origin while keeping the canonical class trivial. More generally, we prove similar extension results for families whose l...

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Bibliographic Details
Published in:Acta mathematica Sinica. English series 2018, Vol.34 (1), p.103-113
Main Authors: Kollár, János, Nicaise, Johannes, Xu, Chen Yang
Format: Article
Language:English
Subjects:
Dimensional stability
Mathematics
Mathematics and Statistics
Series (mathematics)
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Summary:Given a family of Calabi-Yau varieties over the punctured disc or over the field of Laurentseries, we show that, after a finite base change, the family can be extended across the origin while keeping the canonical class trivial. More generally, we prove similar extension results for families whose log-canonical class is semi-ample. We use these to show that the Berkovich and essential skeleta agree for smooth varieties over C（（t）） with semi-ample canonical class.
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-017-7048-8