Serre functor and $\mathbb{P}$-objects for perverse sheaves on $\mathbb{P}^n$
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916782433894400 |
|---|---|
| author | Bonfert, Lukas Cipriani, Alessio |
| author_facet | Bonfert, Lukas Cipriani, Alessio |
| contents | We show that the inverse Serre functor for the constructible derived category $\mathbf{D}^\mathrm{b}_\mathrm{c}(\mathbb{P}^n)$ is given by the $\mathbb{P}$-twist at the simple perverse sheaf corresponding to the open stratum. Moreover, we show that all indecomposable perverse sheaves on $\mathbb{P}^n$ are $\mathbb{P}$-like objects, and explicitly construct morphisms spanning their total endomorphism spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_06051 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Serre functor and $\mathbb{P}$-objects for perverse sheaves on $\mathbb{P}^n$ Bonfert, Lukas Cipriani, Alessio Representation Theory Algebraic Geometry 18G80, 16E35, 14F08 We show that the inverse Serre functor for the constructible derived category $\mathbf{D}^\mathrm{b}_\mathrm{c}(\mathbb{P}^n)$ is given by the $\mathbb{P}$-twist at the simple perverse sheaf corresponding to the open stratum. Moreover, we show that all indecomposable perverse sheaves on $\mathbb{P}^n$ are $\mathbb{P}$-like objects, and explicitly construct morphisms spanning their total endomorphism spaces. |
| title | Serre functor and $\mathbb{P}$-objects for perverse sheaves on $\mathbb{P}^n$ |
| topic | Representation Theory Algebraic Geometry 18G80, 16E35, 14F08 |
| url | https://arxiv.org/abs/2506.06051 |