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K ¨ Ahler Cuts

A symplectic cut of a manifold M with a Hamiltonian circle action is a symplectic quotient of M × C. If M is Kähler then, since C is Kähler, the cut space is Kähler 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 Kähler manifold.