Symplectic resolutions of quiver varieties
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2016
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| _version_ | 1866913433288441856 |
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| author | Bellamy, Gwyn Schedler, Travis |
| author_facet | Bellamy, Gwyn Schedler, Travis |
| contents | In this article, we consider Nakajima quiver varieties from the point of view of symplectic algebraic geometry. We prove that they are all symplectic singularities in the sense of Beauville and completely classify which admit symplectic resolutions. Moreover we show that the smooth locus coincides with the locus of canonically $θ$-polystable points, generalizing a result of Le Bruyn; we study their étale local structure and find their symplectic leaves. An interesting consequence of our results is that not all symplectic resolutions of quiver varieties appear to come from variation of GIT. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1602_00164 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Symplectic resolutions of quiver varieties Bellamy, Gwyn Schedler, Travis Algebraic Geometry Representation Theory 16S80, 17B63 In this article, we consider Nakajima quiver varieties from the point of view of symplectic algebraic geometry. We prove that they are all symplectic singularities in the sense of Beauville and completely classify which admit symplectic resolutions. Moreover we show that the smooth locus coincides with the locus of canonically $θ$-polystable points, generalizing a result of Le Bruyn; we study their étale local structure and find their symplectic leaves. An interesting consequence of our results is that not all symplectic resolutions of quiver varieties appear to come from variation of GIT. |
| title | Symplectic resolutions of quiver varieties |
| topic | Algebraic Geometry Representation Theory 16S80, 17B63 |
| url | https://arxiv.org/abs/1602.00164 |