K\"ahler-Einstein metrics and higher alpha-invariants

TL;DR

This paper establishes a criterion for the existence of K"ahler-Einstein metrics on Fano manifolds using higher algebraic alpha-invariants, linking geometric analysis with algebraic invariants.

Contribution

Introduces a new criterion based on higher alpha-invariants for determining when Fano manifolds admit K"ahler-Einstein metrics.

Findings

Criterion relates alpha-invariants to metric existence

Provides algebraic conditions for K"ahler-Einstein metrics

Bridges algebraic invariants with differential geometry

Abstract

We give a criterion for the existence of a K\"ahler-Einstein metric on a Fano manifold $M$ in terms of the higher algebraic alpha-invariants $\alpha_{m,k}(M)$.