# The essential skeleton of a degeneration of algebraic varieties

@article{Nicaise2013TheES,
title={The essential skeleton of a degeneration of algebraic varieties},
author={J. Nicaise and Johannes Chenyang Xu},
journal={American Journal of Mathematics},
year={2013},
volume={138},
pages={1645 - 1667}
}
• Published 2013
• Mathematics
• American Journal of Mathematics
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 projective $k(\negthinspace(t)\negthinspace)$-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… Expand
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