Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2503.23976 |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
Table des matières:
- Let $\mathcal{L}$ be a rank one local system with field coefficient on the complement $M(\mathcal{A})$ of an essential complex hyperplane arrangement $\mathcal{A}$ in $\mathbb{C}^\ell$. Dimca-Papadima and Randell independently showed that $M(\mathcal{A})$ is homotopy equivalent to a minimal CW-complex. It implies that $\dim H^k(M(\mathcal{A}),\mathcal{L}) \leq b_k(M(\mathcal{A}))$. In this paper, we show that if $\mathcal{A}$ is real, then the inequality holds as equality for some $0\leq k\leq \ell$ if and only if $\mathcal{L}$ is the constant sheaf. The proof is using the descriptions of local system cohomology of $M(\mathcal{A})$ in terms of chambers.