Semi-stable extensions over 1-dimensional bases

János Kollár; Johannes Nicaise; Chen Yang Xu

doi:10.1007/s10114-017-7048-8

Semi-stable extensions over 1-dimensional bases

János Kollár, Johannes Nicaise, Chen Yang Xu

Mathematics

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

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 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 language	English (US)
Pages (from-to)	103-113
Number of pages	11
Journal	Acta Mathematica Sinica, English Series
Volume	34
Issue number	1
DOIs	https://doi.org/10.1007/s10114-017-7048-8
State	Published - Jan 1 2018

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

Keywords

Laurent series
Semi-stable extension
essential skeleton

Access to Document

10.1007/s10114-017-7048-8

Cite this

@article{e2c02fb9469443d480e155f0c7fa56b8,

title = "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 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.",

keywords = "Laurent series, Semi-stable extension, essential skeleton",

author = "J{\'a}nos Koll{\'a}r and Johannes Nicaise and Xu, {Chen Yang}",

note = "Publisher Copyright: {\textcopyright} 2017, Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany.",

year = "2018",

month = jan,

day = "1",

doi = "10.1007/s10114-017-7048-8",

language = "English (US)",

volume = "34",

pages = "103--113",

journal = "Acta Mathematica Sinica, English Series",

issn = "1439-8516",

publisher = "Springer Verlag",

number = "1",

}

TY - JOUR

T1 - Semi-stable extensions over 1-dimensional bases

AU - Kollár, János

AU - Nicaise, Johannes

AU - Xu, Chen Yang

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

KW - Laurent series

KW - Semi-stable extension

KW - essential skeleton

UR - http://www.scopus.com/inward/record.url?scp=85022213273&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85022213273&partnerID=8YFLogxK

U2 - 10.1007/s10114-017-7048-8

DO - 10.1007/s10114-017-7048-8

M3 - Article

AN - SCOPUS:85022213273

SN - 1439-8516

VL - 34

SP - 103

EP - 113

JO - Acta Mathematica Sinica, English Series

JF - Acta Mathematica Sinica, English Series

IS - 1

ER -

Semi-stable extensions over 1-dimensional bases

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this