Jell, Philipp (2020) Constructing smooth and fully faithful tropicalizations for Mumford curves. SELECTA MATHEMATICA-NEW SERIES, 26 (4): 60. ISSN 1022-1824, 1420-9020
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The tropicalization of an algebraic variety X is a combinatorial shadow of X, which is sensitive to a closed embedding of X into a toric variety. Given a good embedding, the tropicalization can provide a lot of information about X. We construct two types of these good embeddings for Mumford curves: fully faithful tropicalizations, which are embeddings such that the tropicalization admits a continuous section to the associated Berkovich space X-an of X, and smooth tropicalizations. We also show that a smooth curve that admits a smooth tropicalization is necessarily a Mumford curve. Our key tool is a variant of a lifting theorem for rational functions on metric graphs.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | COHOMOLOGY; Tropical geometry; Smooth tropical curves; Mumford curves; Extended skeleta; Faithful tropicalization |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics Mathematics > Prof. Dr. Klaus Künnemann |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 16 Mar 2021 08:52 |
| Last Modified: | 16 Mar 2021 08:52 |
| URI: | https://pred.uni-regensburg.de/id/eprint/44036 |
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