Math @ Duke

Publications [#345765] of Joseph D Rabinoff
Papers Published
 Gubler, W; Rabinoff, J; Werner, A, Tropical skeletons,
Annales De L’Institut Fourier, vol. 67 no. 5
(January, 2017),
pp. 19051961 [doi]
(last updated on 2021/12/07)
Abstract: In this paper, we study the interplay between tropical and analytic geometry for closed subschemes of toric varieties. Let K be a complete nonArchimedean 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 KajiwaraPayne 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 multiplicityone 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 HelmKatz.


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