The Geometry of Discotopes
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2021
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866909627538472960 |
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| author | Gesmundo, Fulvio Meroni, Chiara |
| author_facet | Gesmundo, Fulvio Meroni, Chiara |
| contents | We study a class of semialgebraic convex bodies called discotopes. These are instances of zonoids, objects of interest in real algebraic geometry and random geometry. We focus on the face structure and on the boundary hypersurface of discotopes, highlighting interesting birational properties which may be investigated using tools from algebraic geometry. When a discotope is the Minkowski sum of two-dimensional discs, the Zariski closure of its set of extreme points is an irreducible hypersurface. In this case, we provide an upper bound for the degree of the hypersurface, drawing connections to the theory of classical determinantal varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_01241 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The Geometry of Discotopes Gesmundo, Fulvio Meroni, Chiara Algebraic Geometry Metric Geometry 14P10, 52A99, 52A21, 14M12 We study a class of semialgebraic convex bodies called discotopes. These are instances of zonoids, objects of interest in real algebraic geometry and random geometry. We focus on the face structure and on the boundary hypersurface of discotopes, highlighting interesting birational properties which may be investigated using tools from algebraic geometry. When a discotope is the Minkowski sum of two-dimensional discs, the Zariski closure of its set of extreme points is an irreducible hypersurface. In this case, we provide an upper bound for the degree of the hypersurface, drawing connections to the theory of classical determinantal varieties. |
| title | The Geometry of Discotopes |
| topic | Algebraic Geometry Metric Geometry 14P10, 52A99, 52A21, 14M12 |
| url | https://arxiv.org/abs/2111.01241 |