Symplectic resolutions for conical symplectic varieties

2013/10/30 by Michel Brion, Brion, Michel, Baohua Fu +1
Mathematics · #14E15 #14L30 #17B08 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #math.AG #msc:14E15 #msc:14L30 #msc:17B08

paper · pdf · doi:10.48550/arxiv.1310.8193

Final version to appear in IMRN

openalex publication_date 2013/10/30 · arxiv created 2014/04/04 · arxiv updated 2014/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce the notion of a conical symplectic variety, and show that any symplectic resolution of such a variety is isomorphic to the Springer resolution of a nilpotent orbit in a semisimple Lie algebra, composed with a linear projection.

Related

• A characterization of nilpotent orbit closures among symplectic singularities II
• Symplectic resolutions for nilpotent orbits (II)
• Toric varieties and a generalization of the Springer resolution
• Birational geometry in codimension 2 of symplectic resolutions
• Birational geometry of symplectic resolutions of nilpotent orbits II