Intersection Cohomology of Popov–Vinberg Varieties
Abstract
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 $$G = {\text {SL}}_n$$ G = SL n .
Fields of Study & Subjects
Advanced Algebra and Geometry
Algebraic Geometry and Number Theory
Geometry and complex manifolds
Publication details
- Journal / source
- Transformation Groups
- Publisher
- Springer Science and Business Media LLC
- Publication date
- 3 July 2026
- Language
- EN