Kähler quotient

In mathematics, the Kähler quotient of a Kähler manifold V by a compact group acting on V is given by the quotient of a fiber over a fixed point (or more generally a G-orbit) of the moment map V → g* by the action of G. It is a version of the symplectic quotient for Kähler manifolds.

The Kähler quotient by a group G is closely related to the Mumford quotient by a complexification of G.

See also

• Hyperkähler quotient

References

• Mumford, David; Fogarty, J.; Kirwan, F. (1994), Geometric invariant theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (2) [Results in Mathematics and Related Areas (2)], 34 (3rd ed.), Berlin, New York: Springer-Verlag, ISBN 978-3-540-56963-3, MR 1304906