Non-very generic arrangements in low dimension
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2022
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916959321325568 |
|---|---|
| author | Saito, Takuya Settepanella, Simona |
| author_facet | Saito, Takuya Settepanella, Simona |
| contents | The discriminantal arrangement $\mathcal{B}(n,k,\mathcal{A})$ has been introduced by Manin and Schectman in 1989 and it consists of all non-generic translates of a generic arrangement $\mathcal{A}$ of n hyperplanes in a $k$-dimensional space. It is known that its combinatorics depends on the original arrangement A which, following Bayer and Brandt [3], is called very generic if the intersection lattice of the induced discriminantal arrangement has maximum cardinality, non-very generic otherwise. While a complete description of the combinatorics of $\mathcal{B}(n,k,\mathcal{A})$ when $\mathcal{A}$ is very generic is known (see [2]), very few is known in the non-very generic case. Even to provide examples of non very generic arrangements proved to be a non-trivial task (see [17]). In this paper, we characterize, classify and provide examples of non-very generic arrangements in low dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_04794 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Non-very generic arrangements in low dimension Saito, Takuya Settepanella, Simona Combinatorics 52C35, 05B35 The discriminantal arrangement $\mathcal{B}(n,k,\mathcal{A})$ has been introduced by Manin and Schectman in 1989 and it consists of all non-generic translates of a generic arrangement $\mathcal{A}$ of n hyperplanes in a $k$-dimensional space. It is known that its combinatorics depends on the original arrangement A which, following Bayer and Brandt [3], is called very generic if the intersection lattice of the induced discriminantal arrangement has maximum cardinality, non-very generic otherwise. While a complete description of the combinatorics of $\mathcal{B}(n,k,\mathcal{A})$ when $\mathcal{A}$ is very generic is known (see [2]), very few is known in the non-very generic case. Even to provide examples of non very generic arrangements proved to be a non-trivial task (see [17]). In this paper, we characterize, classify and provide examples of non-very generic arrangements in low dimension. |
| title | Non-very generic arrangements in low dimension |
| topic | Combinatorics 52C35, 05B35 |
| url | https://arxiv.org/abs/2202.04794 |