Semi-stable extensions over 1-dimensional bases

Abstract

Given a family of Calabi-Yau varieties over the punctured disc or over the field of Laurent series, we show that, after a finite base change, the family can be exended 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 $\mathbb{C}((t))$ with semi-ample canonical class.

References in corpus (3)

• Desingularization of quasi-excellent schemes in characteristic zero
• Moduli of varieties of general type
• Hulls and Husks

Cited by in corpus (1)

• The Essential Skeleton of a product of degenerations