In mathematics, specifically in complex geometry, the Kähler quotient of a Kähler manifold X {\displaystyle X} by a Lie group G {\displaystyle G} acting on X {\displaystyle X} by preserving the Kähler structure and with moment map μ : X → g ∗ {\displaystyle \mu :X\to {\mathfrak {g}}^{*}} is the quotient μ − 1 / G. Wikipedia