TL;DR
This paper investigates the K-stability of pairs consisting of a Fano variety and a smooth anti-canonical divisor, establishing stability conditions depending on the angle parameter.
Contribution
It proves that such pairs are K-unstable for negative angles and K-semistable at zero angle, clarifying stability behavior in these cases.
Findings
Pairs with X Fano and D smooth anti-canonical divisor are K-unstable for negative angles.
They are K-semistable at zero angle.
Provides conditions for stability based on the angle parameter.
Abstract
We prove that a pair (X, D) with X Fano and D a smooth anti-canonical divisor is K-unstable for negative angles, and K-semistable for zero angle.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Advanced Algebra and Geometry