The GIT aspect of generalized Kähler reduction. I

Abstract

We revisit generalized Kähler reduction introduced by Lin and Tolman in [15] from a viewpoint of geometric invariant theory. It is shown that in the strong Hamiltonian case introduced in the present paper, many well-known conclusions of ordinary Kähler reduction can be generalized without much effort to the generalized setting. It is also shown how generalized holomorphic structures arise naturally from the reduction procedure.

Metric reduction and generalized holomorphic structures

“…The extended G-action is called Hamiltonian if there is an equivariant map µ : M → g * (g * carries the coadjoint action) such that J 2 (V a + ξ a ) = dµ a , a = 1, 2, · · · , dimg (7.2) where µ a = µ(e a ). According to Lemma 4.2 in [16], in terms of the biHermitian data, Eq. (7.2) is equivalent to…”

“…where µ a = µ(e a ). According to Lemma 4.2 in [16], in terms of the biHermitian data, Eq. (7.2) is equivalent to…”