Extremal decompositions of tropical varieties and relations with rigidity theory
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914698291576832 |
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| author | Babaee, Farhad Dewar, Sean Maxwell, James |
| author_facet | Babaee, Farhad Dewar, Sean Maxwell, James |
| contents | Extremality and irreducibility constitute fundamental concepts in mathematics, particularly within tropical geometry. While extremal decomposition is typically computationally hard, this article presents a fast algorithm for identifying the extremal decomposition of tropical varieties with rational balanced weightings. Additionally, we explore connections and applications related to rigidity theory. In particular, we prove that a tropical hypersurface is extremal if and only if it has a unique reciprocal diagram up to homothety. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_00655 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Extremal decompositions of tropical varieties and relations with rigidity theory Babaee, Farhad Dewar, Sean Maxwell, James Algebraic Geometry Combinatorics Metric Geometry 14T10 (Primary) 14T15, 52C25 (Secondary) Extremality and irreducibility constitute fundamental concepts in mathematics, particularly within tropical geometry. While extremal decomposition is typically computationally hard, this article presents a fast algorithm for identifying the extremal decomposition of tropical varieties with rational balanced weightings. Additionally, we explore connections and applications related to rigidity theory. In particular, we prove that a tropical hypersurface is extremal if and only if it has a unique reciprocal diagram up to homothety. |
| title | Extremal decompositions of tropical varieties and relations with rigidity theory |
| topic | Algebraic Geometry Combinatorics Metric Geometry 14T10 (Primary) 14T15, 52C25 (Secondary) |
| url | https://arxiv.org/abs/2403.00655 |