The Futaki invariant on the blowup of K\"ahler surfaces
Haozhao Li, Yalong Shi
TL;DR
This paper derives an expansion formula for Futaki invariants on blown-up K"ahler surfaces, clarifying the balancing condition and connecting with existing results by Arezzo-Pacard and Stoppa.
Contribution
It provides a new explicit expansion formula for Futaki invariants on blowups of K"ahler surfaces, enhancing understanding of stability conditions.
Findings
Expansion formula for Futaki invariants derived
Clarifies the balancing condition in blowup scenarios
Discusses relation with Stoppa's results
Abstract
We prove the expansion formula for the classical Futaki invariants on the blowup of K\"ahler surfaces, which explains the balancing condition of Arezzo-Pacard. The relation with Stoppa's result is also discussed.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Algebraic Geometry and Number Theory