On singular Hilbert schemes of points: Local structures and tautological sheaves
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2021
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910258639667200 |
|---|---|
| author | Hu, Xiaowen |
| author_facet | Hu, Xiaowen |
| contents | We show an intrinsic version of Thomason's fixed-point theorem. Then we determine the local structure of the Hilbert scheme of at most $7$ points in $\mathbb{A}^3$. In particular, we show that in these cases, the points with the same extra dimension have the same singularity type. Using these results, we compute the equivariant Hilbert functions at the singularities and verify a conjecture of Zhou on the Euler characteristics of tautological sheaves on Hilbert schemes of points on $\mathbb{P}^3$ for at most $6$ points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_05236 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On singular Hilbert schemes of points: Local structures and tautological sheaves Hu, Xiaowen Algebraic Geometry Commutative Algebra 14C05, 14C40, 13D40 We show an intrinsic version of Thomason's fixed-point theorem. Then we determine the local structure of the Hilbert scheme of at most $7$ points in $\mathbb{A}^3$. In particular, we show that in these cases, the points with the same extra dimension have the same singularity type. Using these results, we compute the equivariant Hilbert functions at the singularities and verify a conjecture of Zhou on the Euler characteristics of tautological sheaves on Hilbert schemes of points on $\mathbb{P}^3$ for at most $6$ points. |
| title | On singular Hilbert schemes of points: Local structures and tautological sheaves |
| topic | Algebraic Geometry Commutative Algebra 14C05, 14C40, 13D40 |
| url | https://arxiv.org/abs/2101.05236 |