Stable hyperplane arrangements
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866915549528719360 |
|---|---|
| author | Oshima, Toshio |
| author_facet | Oshima, Toshio |
| contents | We classify complex hyperplane arrangements $\mathcal A$ whose intersection posets $L(\mathcal A)$ satisfy $L(\mathcal A)=π_i^{-1}\circπ_i\bigl(L(\mathcal A)\bigr)$ for $i=1,\dots,n$. Here $π_i$ denotes the projection from $\mathbb C^n$ onto $\mathbb C^{n-1}$ defined by that forgets the coordinate $x_i$ of $(x_1,\dots,x_n)\in\mathbb C^n$, and $π_i\bigl(L(\mathcal A)\bigr)=\{π_i(S)\mid S\in L(\mathcal A)\}$. We show that such arrangements $\mathcal A$ arise as pullbacks of the mirror hyperplanes of complex reflection groups of type $A$ or $B$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_11099 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stable hyperplane arrangements Oshima, Toshio Combinatorics 52C35 We classify complex hyperplane arrangements $\mathcal A$ whose intersection posets $L(\mathcal A)$ satisfy $L(\mathcal A)=π_i^{-1}\circπ_i\bigl(L(\mathcal A)\bigr)$ for $i=1,\dots,n$. Here $π_i$ denotes the projection from $\mathbb C^n$ onto $\mathbb C^{n-1}$ defined by that forgets the coordinate $x_i$ of $(x_1,\dots,x_n)\in\mathbb C^n$, and $π_i\bigl(L(\mathcal A)\bigr)=\{π_i(S)\mid S\in L(\mathcal A)\}$. We show that such arrangements $\mathcal A$ arise as pullbacks of the mirror hyperplanes of complex reflection groups of type $A$ or $B$. |
| title | Stable hyperplane arrangements |
| topic | Combinatorics 52C35 |
| url | https://arxiv.org/abs/2510.11099 |