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The essential skeleton of a degeneration of algebraic varieties. (English) Zbl 1375.14092

Summary: 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 \(k((t))\)-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.

MSC:

14G22 Rigid analytic geometry
14E30 Minimal model program (Mori theory, extremal rays)
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
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