Tropical skeletons


Journal Article

© Association des Annales de l'institut Fourier, 2017. In this paper, we study the interplay between tropical and analytic geometry for closed subschemes of toric varieties. Let K be a complete non-Archimedean field, and let X be a closed subscheme of a toric variety over K. We define the tropical skeleton of X as the subset of the associated Berkovich space Xan which collects all Shilov boundary points in the fibers of the Kajiwara-Payne tropicalization map. We develop polyhedral criteria for limit points to belong to the tropical skeleton, and for the tropical skeleton to be closed. We apply the limit point criteria to the question of continuity of the canonical section of the tropicalization map on the multiplicity-one locus. This map is known to be continuous on all torus orbits; we prove criteria for continuity when crossing torus orbits. When X is schön and defined over a discretely valued field, we show that the tropical skeleton coincides with a skeleton of a strictly semistable pair, and is naturally isomorphic to the parameterizing complex of Helm-Katz.

Full Text

Duke Authors

Cited Authors

  • Gubler, W; Rabinoff, J; Werner, A

Published Date

  • January 1, 2017

Published In

Volume / Issue

  • 67 / 5

Start / End Page

  • 1905 - 1961

International Standard Serial Number (ISSN)

  • 0373-0956

Digital Object Identifier (DOI)

  • 10.5802/aif.3125

Citation Source

  • Scopus