Equivariant geometry of symmetric quiver orbit closures
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909470575034368 |
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| author | Kinser, Ryan Lanini, Martina Rajchgot, Jenna |
| author_facet | Kinser, Ryan Lanini, Martina Rajchgot, Jenna |
| contents | We unify problems about the equivariant geometry of symmetric quiver representation varieties, in the finite type setting, with the corresponding problems for symmetric varieties $GL(n)/K$ where $K$ is an orthogonal or symplectic group. In particular, we translate results about singularities of orbit closures; combinatorics of orbit closure containment; and torus equivariant cohomology and K-theory between these classes of varieties. We obtain these results by constructing explicit embeddings with nice properties of homogeneous fiber bundles over type $A$ symmetric quiver representation varieties into symmetric varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_06929 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Equivariant geometry of symmetric quiver orbit closures Kinser, Ryan Lanini, Martina Rajchgot, Jenna Algebraic Geometry Combinatorics Representation Theory 16G20, 14M12, 13C40, 14M27 We unify problems about the equivariant geometry of symmetric quiver representation varieties, in the finite type setting, with the corresponding problems for symmetric varieties $GL(n)/K$ where $K$ is an orthogonal or symplectic group. In particular, we translate results about singularities of orbit closures; combinatorics of orbit closure containment; and torus equivariant cohomology and K-theory between these classes of varieties. We obtain these results by constructing explicit embeddings with nice properties of homogeneous fiber bundles over type $A$ symmetric quiver representation varieties into symmetric varieties. |
| title | Equivariant geometry of symmetric quiver orbit closures |
| topic | Algebraic Geometry Combinatorics Representation Theory 16G20, 14M12, 13C40, 14M27 |
| url | https://arxiv.org/abs/2410.06929 |