Hultgren, Jakob and Jonsson, Mattias and Mazzon, Enrica and McCleerey, Nicholas (2024) Tropical and non-Archimedean Monge-Ampère equations for a class of Calabi-Yau hypersurfaces. ADVANCES IN MATHEMATICS, 439: 109494. ISSN 0001-8708, 1090-2082
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For a large class of maximally degenerate families of Calabi- Yau hypersurfaces of complex projective space, we study nonArchimedean and tropical Monge-Ampere equations, taking place on the associated Berkovich space, and the essential skeleton therein, respectively. For a symmetric measure on the skeleton, we prove that the tropical equation admits a unique solution, up to an additive constant. Moreover, the solution to the non-Archimedean equation can be derived from the tropical solution, and is the restriction of a continuous semipositive toric metric on projective space. Together with the work of Yang Li, this implies the weak metric SYZ conjecture on the existence of special Lagrangian fibrations in our setting. (c) 2024 Elsevier Inc. All rights reserved.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | MIRROR SYMMETRY; DEGENERATION; LIMITS; Calabi-Yau manifolds; SYZ conjecture; Essential skeleton; Monge-Ampere equations; Special Lagrangian fibration |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 15 Jul 2025 07:54 |
| Last Modified: | 15 Jul 2025 07:54 |
| URI: | https://pred.uni-regensburg.de/id/eprint/64797 |
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