The GIT aspect of generalized K$\ddot{a}$hler reduction. I

TL;DR

This paper explores generalized Kähler reduction through geometric invariant theory, demonstrating that many classical results extend to this broader context and revealing how generalized holomorphic structures emerge naturally.

Contribution

It introduces the strong Hamiltonian case in generalized Kähler reduction and shows how classical Kähler reduction results generalize without much effort.

Findings

Classical Kähler reduction results extend to generalized Kähler setting.

Generalized holomorphic structures naturally arise from the reduction process.

The strong Hamiltonian case simplifies the generalization of known results.

Abstract

We revisit generalized K$\ddot{a}$hler reduction introduced by Lin and Tolman in \cite{LT} 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 K$\ddot{a}$hler 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.