Gubler, Walter and Rabinoff, Joseph and Werner, Annette (2017) TROPICAL SKELETONS. ANNALES DE L INSTITUT FOURIER, 67 (5). pp. 1905-1961. ISSN 0373-0956,
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In this paper, we study the interplay between tropical and analytic geometry for closed subschemes of toric varieties. Let K be a complete non-Archiinedean 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 X-an 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 schon 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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ARCHIMEDEAN ANALYTIC SPACES; FAITHFUL TROPICALIZATION; BERKOVICH SPACES; RIGID-SPACES; GEOMETRY; CURVES; INTERSECTIONS; COMPACTIFICATIONS; VARIETIES; Tropical geometry; Kajiwara-Payne tropicalization; Berkovich spaces; skeletons |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Walter Gubler |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 14 Dec 2018 13:01 |
| Last Modified: | 28 Feb 2019 09:43 |
| URI: | https://pred.uni-regensburg.de/id/eprint/587 |
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