Semi-stable extensions over 1-dimensional bases

János Kollár, Johannes Nicaise, Chen Yang Xu

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


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 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.

Original languageEnglish (US)
Pages (from-to)103-113
Number of pages11
JournalActa Mathematica Sinica, English Series
Issue number1
StatePublished - Jan 1 2018

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


  • Laurent series
  • Semi-stable extension
  • essential skeleton


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