Phase limit sets of linear spaces and discriminants
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909407932055552 |
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| author | Nisse, Mounir Sottile, Frank |
| author_facet | Nisse, Mounir Sottile, Frank |
| contents | We show that the closure of the coamoeba of a linear space/hyperplane complement is the union of products of coamoebas of hyperplane complements coming from flags of flats, and relate this to the Bergman fan. Using the Horn-Kapranov parameterization of a reduced discriminant, this gives a partial description of the phase limit sets of discriminants and duals of toric varieties. When d=3, we show that each 3-dimensional component of the phase limit set of the discriminant is a prism over a discriminant coamoeba in dimension 2, which has a polyhedral description by a result of Nilsson and Passare. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_19018 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Phase limit sets of linear spaces and discriminants Nisse, Mounir Sottile, Frank Algebraic Geometry Combinatorics 14T15, 14T20, 32A60, 52C35 We show that the closure of the coamoeba of a linear space/hyperplane complement is the union of products of coamoebas of hyperplane complements coming from flags of flats, and relate this to the Bergman fan. Using the Horn-Kapranov parameterization of a reduced discriminant, this gives a partial description of the phase limit sets of discriminants and duals of toric varieties. When d=3, we show that each 3-dimensional component of the phase limit set of the discriminant is a prism over a discriminant coamoeba in dimension 2, which has a polyhedral description by a result of Nilsson and Passare. |
| title | Phase limit sets of linear spaces and discriminants |
| topic | Algebraic Geometry Combinatorics 14T15, 14T20, 32A60, 52C35 |
| url | https://arxiv.org/abs/2411.19018 |