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 cla...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.展开更多
基金support was provided to JK by the NSF under grant number DMS-1362960Starting Grant MOTZETA(Grant No.306610)of the European Research Council Chinese National Science Fund for Distinguished Young Scholars(Grant No.11425101)
文摘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.
