Kaehlerian reduction in steps

TL;DR

This paper investigates the process of Kaehlerian reduction in steps for Hamiltonian actions of compact Lie groups on Kaehler manifolds, establishing a stratified structure and isomorphisms in the reduction process.

Contribution

It introduces a stepwise reduction framework for Kaehlerian reduction involving normal subgroups, revealing a stratified structure and natural isomorphisms.

Findings

Kaehlerian reduction with respect to a normal subgroup yields a stratified Hamiltonian Kaehler space.

The reduction with respect to the quotient group is naturally isomorphic to the original reduction.

The work extends the understanding of reduction procedures in complex geometric settings.

Abstract

We study Hamiltonian actions of compact Lie groups K on Kaehler manifolds which extend to a holomorphic action of the complexified group K^C. For a closed normal subgroup L of K we show that the Kaehlerian reduction with respect to L is a stratified Hamiltonian Kaehler K^C/L^C-space whose Kaehlerian reduction with respect to K/L is naturally isomorphic to the Kaehlerian reduction of the original manifold with respect to K.