The essential skeleton of a degeneration of algebraic varieties

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.

To appear in American Journal of Mathematics

Cited by in corpus (6)

• Poles of maximal order of motivic zeta functions
• Families of Calabi-Yau manifolds and canonical singularities
• Hybrid convergence of Kähler-Einstein measures
• Berkovich skeleta and birational geometry
• Triangulations of non-archimedean curves, semi-stable reduction, and ramification
• Topology of nonarchimedean analytic spaces and relations to complex algebraic geometry