Intersection cohomology of Vinberg-Popov varieties
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909699067084800 |
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| author | Dancer, Andrew Martens, Johan Proudfoot, Nicholas |
| author_facet | Dancer, Andrew Martens, Johan Proudfoot, Nicholas |
| contents | The Vinberg-Popov variety of a simply connected reductive algebraic group $G$ is a singular affine variety that contains the basic affine space $G/U$ as a Zariski open subset. It is defined as the spectrum of the ring of functions on $G/U$, and can also be identified with the universal symplectic implosion for the maximal compact subgroup of $G$. We provide a recursive procedure for computing the intersection cohomology of this variety, with an emphasis on the case where $G = \operatorname{SL}_n$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_16492 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Intersection cohomology of Vinberg-Popov varieties Dancer, Andrew Martens, Johan Proudfoot, Nicholas Algebraic Geometry Representation Theory Symplectic Geometry The Vinberg-Popov variety of a simply connected reductive algebraic group $G$ is a singular affine variety that contains the basic affine space $G/U$ as a Zariski open subset. It is defined as the spectrum of the ring of functions on $G/U$, and can also be identified with the universal symplectic implosion for the maximal compact subgroup of $G$. We provide a recursive procedure for computing the intersection cohomology of this variety, with an emphasis on the case where $G = \operatorname{SL}_n$. |
| title | Intersection cohomology of Vinberg-Popov varieties |
| topic | Algebraic Geometry Representation Theory Symplectic Geometry |
| url | https://arxiv.org/abs/2507.16492 |