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Semi-stable extensions over 1-dimensional bases. (English) Zbl 1408.14061

The authors show that, after a finite base change, any family of Calabi-Yau varieties over the punctured disc or over the field of Laurent series, can be exended across the origin in such a way that the canonical class is trivial and the special fiber has mild singularities. They also prove a similar extension results for families (with mild singularities) whose log-canonical class is semi-ample and use this result to to show that the Berkovich and essential skeleta agree for smooth varieties over \(\mathbb C((t))\) with semi-ample canonical class.

MSC:

14E30 Minimal model program (Mori theory, extremal rays)
14G22 Rigid analytic geometry
14J10 Families, moduli, classification: algebraic theory
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
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