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arXiv · 2507.16492

Intersection cohomology of Popov-Vinberg varieties

Andrew Dancer·Johan Martens·Nicholas Proudfoot
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Abstract

The Popov-Vinberg variety of a simply connected, split, semisimple 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 $G = \operatorname{SL}_n$.

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Andrew Dancer, Johan Martens, Nicholas Proudfoot. 2025-07-22. Intersection cohomology of Popov-Vinberg varieties. https://doi.org/10.1007/s00031-026-09982-y

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