Note on geodesic rays tamed by simple test configurations

TL;DR

This paper provides a new proof of a theorem regarding the existence of smooth geodesic rays controlled by specific degenerations, contributing to the understanding of geometric structures in complex geometry.

Contribution

It offers a novel proof of Arezzo-Tian's theorem on smooth geodesic rays associated with simple test configurations.

Findings

New proof of Arezzo-Tian's theorem

Clarifies the relationship between geodesic rays and test configurations

Enhances understanding of geometric degenerations

Abstract

In this short note, we give a new proof of a theorem of Arezzo-Tian on the existence of smooth geodesic rays tamed by a special degeneration.