Yau-Tian-Donaldson correspondence for K-semistable Fano manifolds
Chi Li
TL;DR
This paper establishes a key correspondence in complex geometry linking K-semistability and the existence of special metrics on Fano manifolds, building on recent compactness results.
Contribution
It proves the K-semistable version of the Yau-Tian-Donaldson conjecture for Fano manifolds, extending previous results to a broader stability condition.
Findings
Proves the K-semistable Yau-Tian-Donaldson correspondence for Fano manifolds
Utilizes recent compactness results of Tian and Chen-Donaldson-Sun
Advances understanding of stability conditions in complex geometry
Abstract
In this note, using the recent compactness results of Tian and Chen-Donaldson-Sun, we prove the K-semistable version of Yau-Tian-Donaldson correspondence for Fano manifolds.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Algebraic Geometry and Number Theory