On the K‐stability of blow‐ups of projective bundles
Abstract
Abstract We investigate the K‐stability of certain blow‐ups of ‐bundles over a Fano variety , where the ‐bundle is the projective compactification of a line bundle proportional to and the center of the blow‐up is the image along a positive section of a divisor also proportional to . When and are smooth, we show that, for , the K‐semistability and K‐polystability of the blow‐up are equivalent to the K‐semistability and K‐polystability of the log Fano pair for some coefficient explicitly computed. We also show that, for , , the blow‐up is K‐unstable.
Fields of Study & Subjects
Geometry and complex manifolds
Algebraic Geometry and Number Theory
Geometric Analysis and Curvature Flows
Publication details
- Journal / source
- Journal of the London Mathematical Society
- Volume
- 113
- Issue
- 5
- Publication date
- 1 May 2026
- Language
- EN