Rank 4 stable vector bundles on hyperkähler fourfolds of Kummer type
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918524011675648 |
|---|---|
| author | O'Grady, Kieran G. |
| author_facet | O'Grady, Kieran G. |
| contents | We partially extend to hyperkähler fourfolds of Kummer type the results that we have proved regarding stable rigid vector bundles on hyperkähler (HK) varieties of type $K3^{[n]}$. Let $(M,h)$ be a general polarized HK fourfold of Kummer type such that $q_M(h)\equiv -6\pmod{16}$ and the divisibility of $h$ is $2$, or $q_M(h)\equiv -6\pmod{144}$ and the divisibility of $h$ is $6$. We show that there exists a unique (up to isomorphism) slope stable vector bundle $\cal F$ on $M$ such that $r({\cal F})=4$, $ c_1({\cal F})=h$, $Δ({\cal F})=c_2(M)$. Moreover $\cal F$ is rigid. One of our motivations is the desire to describe explicitly a locally complete family of polarized HK fourfolds of Kummer type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_03987 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Rank 4 stable vector bundles on hyperkähler fourfolds of Kummer type O'Grady, Kieran G. Algebraic Geometry 14J42 (Primary), 14J60 (Secondary) We partially extend to hyperkähler fourfolds of Kummer type the results that we have proved regarding stable rigid vector bundles on hyperkähler (HK) varieties of type $K3^{[n]}$. Let $(M,h)$ be a general polarized HK fourfold of Kummer type such that $q_M(h)\equiv -6\pmod{16}$ and the divisibility of $h$ is $2$, or $q_M(h)\equiv -6\pmod{144}$ and the divisibility of $h$ is $6$. We show that there exists a unique (up to isomorphism) slope stable vector bundle $\cal F$ on $M$ such that $r({\cal F})=4$, $ c_1({\cal F})=h$, $Δ({\cal F})=c_2(M)$. Moreover $\cal F$ is rigid. One of our motivations is the desire to describe explicitly a locally complete family of polarized HK fourfolds of Kummer type. |
| title | Rank 4 stable vector bundles on hyperkähler fourfolds of Kummer type |
| topic | Algebraic Geometry 14J42 (Primary), 14J60 (Secondary) |
| url | https://arxiv.org/abs/2203.03987 |