2022/08/01 by Brian Weber, Weber, Brian
Mathematics · #53C55 #58J05 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2208.00997
openalex publication_date 2022/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The symplectic reduction of a complete toric Kähler manifold need not be closed or even be a polygon. Sharp differences in behavior occur between those complete toric Kähler 4-manifolds with closed and with non-closed reductions. This paper establishes geometric criteria for these reductions to be closed, and classifies all asymptotic geometries possible in the case of scalar-flat instantons with closed reductions. Contrasting this, we provide examples of complete instantons with non-closed and non-polygon reductions.