Gil, Jose Ignacio Burgos and Gubler, Walter and Jell, Philipp and Kuennemann, Klaus (2025) Pluripotential theory for tropical toric varieties and non-Archimedean Monge-Ampère equations. KYOTO JOURNAL OF MATHEMATICS, 65 (1). pp. 55-152. ISSN 2156-2261, 2154-3321
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Tropical toric varieties are partial compactifications of finite dimensional real vector spaces associated with rational polyhedral fans. We introduce plurisubharmonic functions and a Bedford-Taylor product for Lagerb erg currents on open subsets of a tropical toric variety. The resulting tropical toric pluripotential theory provides the link to give a canonical correspondence between complex and non-Archimedean pluripotential theories of invariant plurisubharmonic functions on toric varieties. We will apply this correspondence to solve invariant non-Archimedean Monge-Ampe`re equations on toric and abelian varieties over arbitrary non-Archimedean fields.
| Item Type: | Article |
|---|---|
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Klaus Künnemann Mathematics > Prof. Dr. Walter Gubler |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 23 Jun 2026 06:48 |
| Last Modified: | 23 Jun 2026 06:48 |
| URI: | https://pred.uni-regensburg.de/id/eprint/66623 |
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