Research Paper#Complex Geometry, Kähler-Einstein Geometry, Vector Bundles🔬 ResearchAnalyzed: Jan 3, 2026 17:02
Admissible HYM Metrics and MY Equality on Klt Varieties
Published:Dec 30, 2025 11:47
•1 min read
•ArXiv
Analysis
This paper presents three key results in the realm of complex geometry, specifically focusing on Kähler-Einstein (KE) varieties and vector bundles. The first result establishes the existence of admissible Hermitian-Yang-Mills (HYM) metrics on slope-stable reflexive sheaves over log terminal KE varieties. The second result connects the Miyaoka-Yau (MY) equality for K-stable varieties with big anti-canonical divisors to the existence of quasi-étale covers from projective space. The third result provides a counterexample regarding semistability of vector bundles, demonstrating that semistability with respect to a nef and big line bundle does not necessarily imply semistability with respect to ample line bundles. These results contribute to the understanding of stability conditions and metric properties in complex geometry.
Key Takeaways
- •Establishes the existence of admissible HYM metrics under specific stability conditions.
- •Connects the MY equality to the existence of quasi-étale covers.
- •Provides a counterexample regarding semistability of vector bundles.
Reference
“If a reflexive sheaf $\mathcal{E}$ on a log terminal Kähler-Einstein variety $(X,ω)$ is slope stable with respect to a singular Kähler-Einstein metric $ω$, then $\mathcal{E}$ admits an $ω$-admissible Hermitian-Yang-Mills metric.”