Asymptotic geometry of toric Kahler instantons

Abstract

The symplectic reduction of a complete toric K\"ahler manifold need not be closed or even be a polygon. Sharp differences in behavior occur between those complete toric K\"ahler 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.