The essential skeleton of a degeneration of algebraic varieties
By Johannes Nicaise, Chenyang Xu. 2013
92 citations recorded by the source corpus.
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 essential skeleton of a Calabi-Yau variety over $k(\negthinspace(t)\negthinspace)$ is a pseudo-manifold.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/a9b039a29fe2f1e04a6d4ed57cbd47fdf1d57895
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Tropical and non-Archimedean limits of degenerating families of volume forms (2016, background): “t; the degeneration is. Further, the family X!D admits a relative minimal model X, with certain mild (dlt) singularities [KNX15], and the essential skeleton can be identied with the dual complex of X[NX13]. In particular, d= 0 if and only if Xcan lled in with a central ber X 0 which is a Calabi{Yau ”
- Theta functions on varieties with effective anti-canonical class (2016, unknown): “NS 5 a dlt minimal model of a maximally unipotent degeneration of Calabi-Yau varieties. Koll´ar and Xu in [KoXu], §33 showed that Bwill indeed be a manifold off of a codimension three subset (see also [NX] for somewhat weaker results). The parameterizing family Sfor our construction then arises by ch”