About: Kähler quotient

In mathematics, specifically in complex geometry, the Kähler quotient of a Kähler manifold by a Lie group acting on by preserving the Kähler structure and with moment map (with respect to the Kähler form) is the quotient If acts freely and properly, then is a new Kähler manifold whose Kähler form is given by the symplectic quotient construction. By the Kempf-Ness theorem, a Kähler quotient by a compact Lie group is closely related to a geometric invariant theory quotient by the complexification of .