Real and Positive Tropicalizations of Symmetric Determinantal Varieties
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914957684113408 |
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| author | Ahmadieh, Abeer Al Cai, May Yu, Josephine |
| author_facet | Ahmadieh, Abeer Al Cai, May Yu, Josephine |
| contents | We study real and positive tropicalizations of the varieties of low rank symmetric matrices over real or complex Puiseux series. We show that real tropicalization coincides with complex tropicalization for rank two and corank one cases. We also show that the two notions of positive tropicalization introduced by Speyer and Williams coincide for symmetric rank two matrices, but they differ for symmetric corank one matrices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_17462 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Real and Positive Tropicalizations of Symmetric Determinantal Varieties Ahmadieh, Abeer Al Cai, May Yu, Josephine Algebraic Geometry Combinatorics We study real and positive tropicalizations of the varieties of low rank symmetric matrices over real or complex Puiseux series. We show that real tropicalization coincides with complex tropicalization for rank two and corank one cases. We also show that the two notions of positive tropicalization introduced by Speyer and Williams coincide for symmetric rank two matrices, but they differ for symmetric corank one matrices. |
| title | Real and Positive Tropicalizations of Symmetric Determinantal Varieties |
| topic | Algebraic Geometry Combinatorics |
| url | https://arxiv.org/abs/2409.17462 |