A smooth but non-symplectic moduli of sheaves on a hyperkähler variety
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929499675820032 |
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| author | Krug, Andreas Reede, Fabian Zhang, Ziyu |
| author_facet | Krug, Andreas Reede, Fabian Zhang, Ziyu |
| contents | For an abelian surface $A$, we consider stable vector bundles on a generalized Kummer variety $K_n(A)$ with $n>1$. We prove that the connected component of the moduli space which contains the tautological bundles associated to line bundles of degree $0$ is isomorphic to the blowup of the dual abelian surface in one point. We believe that this is the first explicit example of a component which is smooth with a non-trivial canonical bundle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08991 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A smooth but non-symplectic moduli of sheaves on a hyperkähler variety Krug, Andreas Reede, Fabian Zhang, Ziyu Algebraic Geometry For an abelian surface $A$, we consider stable vector bundles on a generalized Kummer variety $K_n(A)$ with $n>1$. We prove that the connected component of the moduli space which contains the tautological bundles associated to line bundles of degree $0$ is isomorphic to the blowup of the dual abelian surface in one point. We believe that this is the first explicit example of a component which is smooth with a non-trivial canonical bundle. |
| title | A smooth but non-symplectic moduli of sheaves on a hyperkähler variety |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2409.08991 |