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The essential skeleton of a degeneration of algebraic varieties

JOHANNES NICAISE CHENYANG XU Peking University

mathscidoc:1707.01001

Distinguished Paper Award in 2017

Amer. J. Math., 138, (6), 1645--1667, 2016
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 letX be a smooth and projective 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.
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@inproceedings{johannes2016the,
  title={The essential skeleton of a degeneration of algebraic varieties},
  author={JOHANNES NICAISE, and CHENYANG XU},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170719185754047657800},
  booktitle={Amer. J. Math.},
  volume={138},
  number={6},
  pages={1645--1667},
  year={2016},
}
JOHANNES NICAISE, and CHENYANG XU. The essential skeleton of a degeneration of algebraic varieties. 2016. Vol. 138. In Amer. J. Math.. pp.1645--1667. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170719185754047657800.
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