English

Semi-stable extensions over 1-dimensional bases

Algebraic Geometry 2015-10-09 v1

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 C((t)){\mathbb C}((t)) with semi-ample canonical class.

Keywords

Cite

@article{arxiv.1510.02446,
  title  = {Semi-stable extensions over 1-dimensional bases},
  author = {János Kollár and Johannes Nicaise and Chenyang Xu},
  journal= {arXiv preprint arXiv:1510.02446},
  year   = {2015}
}
R2 v1 2026-06-22T11:16:02.384Z