Generalized K\"ahler Einstein metrics and uniform stability for toric Fano manifolds

TL;DR

This paper establishes a criterion linking the existence of generalized Kähler Einstein metrics on toric Fano manifolds with uniform stability and the properness of a certain functional, bridging geometric analysis and algebraic stability.

Contribution

It provides a complete criterion connecting the existence of generalized Kähler Einstein metrics with uniform stability and functional properness on toric Fano manifolds.

Findings

Criterion for existence of generalized Kähler Einstein metrics

Connection between stability and metric existence

Functional properness as a stability indicator

Abstract

We give a complete criterion for the existence of generalized K\"ahler Einstein metrics on toric Fano manifolds from view points of a uniform stability in a sense of GIT and the properness of a functional on the space of K\"ahler metrics.