Fundamentals of Broken Line Convex Geometry
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| author | Frías-Medina, Juan Bosco Magee, Timothy |
| author_facet | Frías-Medina, Juan Bosco Magee, Timothy |
| contents | We develop the fundamentals of a new theory of convex geometry -- which we call "broken line convex geometry". This is a theory of convexity where the ambient space is the rational tropicalization of a cluster variety, as opposed to an ambient vector space. In this theory, line segments are replaced by broken line segments, and we adopt the notion of convexity in [CMN21]. We state and prove broken line convex geometry versions of many standard results from usual convex geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_02427 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fundamentals of Broken Line Convex Geometry Frías-Medina, Juan Bosco Magee, Timothy Algebraic Geometry Combinatorics Primary: 52A01, Secondary: 14J33, 14M99, 13F60, 51M20 We develop the fundamentals of a new theory of convex geometry -- which we call "broken line convex geometry". This is a theory of convexity where the ambient space is the rational tropicalization of a cluster variety, as opposed to an ambient vector space. In this theory, line segments are replaced by broken line segments, and we adopt the notion of convexity in [CMN21]. We state and prove broken line convex geometry versions of many standard results from usual convex geometry. |
| title | Fundamentals of Broken Line Convex Geometry |
| topic | Algebraic Geometry Combinatorics Primary: 52A01, Secondary: 14J33, 14M99, 13F60, 51M20 |
| url | https://arxiv.org/abs/2407.02427 |