Kähler quotient

In mathematics, specifically in complex geometry, the Kähler quotient of a Kähler manifold

by preserving the Kähler structure and with moment map

(with respect to the Kähler form) is the quotient If

[1] 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