Intersection cohomology of Popov-Vinberg varieties

Journal article

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=SLn.

Authors: Dancer, A; Martens, J; Proudfoot, N

• Publication status: Accepted
• Peer review status: Peer reviewed
• Publisher: Springer
• Journal: Transformation Groups
• Acceptance date: 2026-06-12
• EISSN: 1531-586X
• ISSN: 1083-4362
• Language: English