2002/12/04 by D. Burns, V. Guillemin, Burns, D. +3
Mathematics · #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG) #math.CV #math.DG #math.SG
paper · pdf · doi:10.48550/arxiv.math/0212062
14 pages
arxiv created 2002/12/04 · arxiv updated 2009/11/30
A symplectic cut of a manifold M with a Hamiltonian circle action is a symplectic quotient of M x C. If M is Kaehler then, since C is Kaehler, the cut space is Kaehler as well. The symplectic structure on the cut is well understood. In this paper we describe the complex structure (and hence the metric) on the cut. We then generalize the construction to the case where M has a torus action and C is replaced by a toric Kaehler manifold.