K\"ahler geometry on complex projective spaces via reduction and unfolding

TL;DR

This paper reviews methods using reduction and unfolding procedures to describe the K"ahler geometry of complex projective spaces, providing a geometric framework for understanding their structure.

Contribution

It introduces a unified approach combining reduction and unfolding techniques to analyze K"ahler geometry on complex projective spaces.

Findings

Describes the K"ahler structure via principal fibration reduction

Uses momentum maps to facilitate unfolding procedures

Provides a geometric interpretation of complex projective spaces

Abstract

We review how a reduction procedure along a principal fibration and an unfolding procedure associated to a suitable momentum map allow to describe the K\"ahler geometry of a finite dimensional complex projective spaces.