Modular sheaves with many moduli
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915740928442368 |
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| author | O'Grady, Kieran G. |
| author_facet | O'Grady, Kieran G. |
| contents | We exhibit moduli spaces of slope stable vector bundles on general polarized HK varieties $(X,h)$ of type $K3^{[2]}$ which have an irreducible component of dimension $2a^2+2$, with $a$ an arbitrary integer greater than $1$. This is done by studying the case $X=S^{[2]}$ where $S$ is an elliptic $K3$ surface. We show that in this case there is an irreducible component of the moduli space of stable vector bundles on $S^{[2]}$ which is birational to a moduli space of sheaves on $S$. We expect that if the moduli space of sheaves on $S$ is a smooth HK variety (necessarily of type $K3^{[a^2+1]}$) then the following more precise version holds: the closure of the moduli space of slope stable vector bundles on $(X,h)$ in the moduli space of Gieseker-Maruyama semistable sheaves with its GIT polarization is a general polarized HK variety of type $K3^{[a^2+1]}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_18101 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Modular sheaves with many moduli O'Grady, Kieran G. Algebraic Geometry 14J42, 14J60 We exhibit moduli spaces of slope stable vector bundles on general polarized HK varieties $(X,h)$ of type $K3^{[2]}$ which have an irreducible component of dimension $2a^2+2$, with $a$ an arbitrary integer greater than $1$. This is done by studying the case $X=S^{[2]}$ where $S$ is an elliptic $K3$ surface. We show that in this case there is an irreducible component of the moduli space of stable vector bundles on $S^{[2]}$ which is birational to a moduli space of sheaves on $S$. We expect that if the moduli space of sheaves on $S$ is a smooth HK variety (necessarily of type $K3^{[a^2+1]}$) then the following more precise version holds: the closure of the moduli space of slope stable vector bundles on $(X,h)$ in the moduli space of Gieseker-Maruyama semistable sheaves with its GIT polarization is a general polarized HK variety of type $K3^{[a^2+1]}$. |
| title | Modular sheaves with many moduli |
| topic | Algebraic Geometry 14J42, 14J60 |
| url | https://arxiv.org/abs/2407.18101 |