On the K‐stability of blow‐ups of projective bundles
Daniel Mallory
Source 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.
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