2011/01/26 by Craig van Coevering, Wei Zhang, van Coevering, Craig +1
Mathematics · #14L24 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Primary 53C26 #Secondary 53D20 #Symplectic Geometry (math.SG) #math.AG #math.DG #math.SG #msc:14L24 #msc:53C26 #msc:53D20
paper · pdf · doi:10.48550/arxiv.1101.5050
16 pages, 4 figure
openalex publication_date 2011/01/26 · arxiv created 2011/07/01 · arxiv updated 2015/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Toric hyperkähler manifolds are quaternion analog of toric varieties. Bielawski pointed out that they can be glued by cotangent bundles of toric varieties. Following his idea, viewing both toric varieties and toric hyperkäher manifolds as GIT quotients, we first establish geometrical criteria for the semi-stable points. Then based on these criteria, we show that the cotangent bundles of compact toric varieties in the core of toric hyperkähler manifold are sufficient to glue the desired toric hyperkähler manifold.