The essential skeleton of a degeneration of algebraic varieties

Johannes Nicaise; Chenyang Xu

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arXiv · 1307.4041

The essential skeleton of a degeneration of algebraic varieties

Johannes Nicaise·Chenyang Xu

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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.

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Johannes Nicaise, Chenyang Xu. 2013-07-15. The essential skeleton of a degeneration of algebraic varieties. https://arxiv.org/abs/1307.4041

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