Kähler quotient explained

X by a Lie group G acting on X by preserving the Kähler structure and with moment map \mu : X \to ak{g} ^{*} (with respect to the Kähler form) is the quotient\mu ^{-1} ( 0 )/G.

If

G acts freely and properly, then \mu ^{-1} ( 0 )/G is a new Kähler manifold whose Kähler form is given by the symplectic quotient construction.G is closely related to a geometric invariant theory quotient by the complexification of G .

See also

• Hyperkähler quotient