Tian's invariant of the Grassmann manifold

TL;DR

This paper establishes that Tian's invariant for the complex Grassmann manifold $G_{p, q}(\,mathbb{C})$ is exactly $1/(p+q)$, providing a precise value for this geometric invariant.

Contribution

The paper computes the exact value of Tian's invariant for complex Grassmann manifolds, filling a gap in the understanding of their geometric properties.

Findings

Tian's invariant for $G_{p, q}(\mathbb{C})$ is $1/(p+q)$

Provides a precise value for Tian's invariant on Grassmannians

Enhances understanding of geometric invariants of complex manifolds

Abstract

We prove that Tian's invariant on the complex Grassmann manifold $G_{p, q}(\mathbb{C})$ is equal to $1/(p+q)$.