2007/01/31 by Kyo Nishiyama
Mathematics · #Advanced Algebra and Geometry #Algebraic geometry #Differential geometry #Equivariant map #Geometric and Algebraic Topology #Grassmannian #Gravitational singularity #Homotopy and Cohomology in Algebraic Topology #Null (SQL) #Resolution (logic) #Resolution of singularities #Vector bundle #math.AG #math.RT #msc:14E15 #msc:14L30 #msc:14M15 #msc:20G05 #msc:22E47
paper · pdf · doi:10.1007/s10711-009-9369-y
published as Geometriae Dedicata, 143(2009), no.~1, 19 -- 35 · 17 pages; completely revised and add references
arxiv created 2007/12/28 · openalex publication_date 2009/04/21 · arxiv updated 2010/12/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study the null fiber of a moment map related to dual pairs. We construct an equivariant resolution of singularities of the null fiber, and get conormal bundles of closed KC -orbits in the Lagrangian Grassmannian as the categorical quotient. The conormal bundles thus obtained turn out to be a resolution of singularities of the closure of nilpotent KC -orbits, which is a "quotient" of the resolution of the null fiber.