Enriques surfaces with trivial Brauer map and involutions on hyperkähler manifolds
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929240921866240 |
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| author | Reede, Fabian |
| author_facet | Reede, Fabian |
| contents | Let $X$ be an Enriques surface. Using Beauville's result about the triviality of the Brauer map of $X$, we define a new involution on the category of coherent sheaves on the canonically covering K3 surface $\overline{X}$. We relate the fixed locus of this involution to certain Picard schemes of the noncommutative pair $(X,\mathcal{A})$, where $\mathcal{A}$ is an Azumaya algebra on $X$ defined by the nontrivial element in the Brauer group of $X$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07611 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Enriques surfaces with trivial Brauer map and involutions on hyperkähler manifolds Reede, Fabian Algebraic Geometry Let $X$ be an Enriques surface. Using Beauville's result about the triviality of the Brauer map of $X$, we define a new involution on the category of coherent sheaves on the canonically covering K3 surface $\overline{X}$. We relate the fixed locus of this involution to certain Picard schemes of the noncommutative pair $(X,\mathcal{A})$, where $\mathcal{A}$ is an Azumaya algebra on $X$ defined by the nontrivial element in the Brauer group of $X$. |
| title | Enriques surfaces with trivial Brauer map and involutions on hyperkähler manifolds |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2402.07611 |