The Kähler quotient is a construction in differential geometry and algebraic geometry that allows one to form a new space from a symplectic manifold by quotienting out by a group action. Specifically, it is commonly associated with Kähler manifolds, where the underlying structure combines a symplectic structure and a Riemannian metric that is compatible with the complex structure.
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A Kähler quotient imposes a moment-map level condition and divides by the compact symmetry group. Under suitable stability assumptions it is equivalent to a quotient by the complexified group and inherits a Kähler metric away from singular orbits.