Momentum maps and the K\"ahler property for base spaces of reductive principal bundles

TL;DR

This paper explores the relationship between the K"ahler property of base spaces, momentum maps, and equivariant compactifications in the context of reductive principal bundles, providing examples to demonstrate optimality.

Contribution

It establishes a novel connection between the K"ahler property of base spaces and momentum maps in reductive principal bundles, with comprehensive examples.

Findings

K"ahler property of the base relates to momentum maps

Equivariant compactifications preserve K"ahler structures

Examples show the main results are optimal

Abstract

We investigate the complex geometry of total spaces of reductive principal bundles over compact base spaces and establish a close relation between the K\"ahler property of the base, momentum maps for the action of a maximal compact subgroup on the total space, and the K\"ahler property of special equivariant compactifications. We provide many examples illustrating that the main result is optimal.