The essential skeleton of a degeneration of algebraic varieties
File(s)1307.4041v1.pdf (233.94 KB)
Accepted version
Author(s)
Nicaise, J
Xu, C
Type
Working Paper
Abstract
In this paper, we explore the connections between the Minimal Model Program
and the theory of Berkovich spaces. Let $k$ be a field of characteristic zero
and let $X$ be a smooth and proper $k((t))$-variety with semi-ample canonical
divisor. We prove that the essential skeleton of $X$ coincides with the
skeleton of any minimal $dlt$-model and that it is a strong deformation retract
of the Berkovich analytification of $X$. As an application, we show that the
essential skeleton of a Calabi-Yau variety over $k((t))$ is a pseudo-manifold.
and the theory of Berkovich spaces. Let $k$ be a field of characteristic zero
and let $X$ be a smooth and proper $k((t))$-variety with semi-ample canonical
divisor. We prove that the essential skeleton of $X$ coincides with the
skeleton of any minimal $dlt$-model and that it is a strong deformation retract
of the Berkovich analytification of $X$. As an application, we show that the
essential skeleton of a Calabi-Yau variety over $k((t))$ is a pseudo-manifold.
Date Issued
2016-12-01
Date Acceptance
2015-02-24
Citation
American Journal of Mathematics, 2016, 138 (6), pp.1645-1667
ISSN
1080-6377
Publisher
Johns Hopkins University Press: American Journal of Mathematics
Start Page
1645
End Page
1667
Journal / Book Title
American Journal of Mathematics
Volume
138
Issue
6
Copyright Statement
© The Author
Sponsor
Commission of the European Communities
Identifier
http://arxiv.org/abs/1307.4041v2
Grant Number
306610
Subjects
math.AG
math.AG
Publication Status
Published