Relative K-polystability of projective bundles over a curve

Apostolov, Vestislav; Keller, Julien

doi:10.1090/tran/7556

Relative K-polystability of projective bundles over a curve
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by Vestislav Apostolov and Julien Keller PDF

Trans. Amer. Math. Soc. 372 (2019), 233-266 Request permission

Abstract:

Let $\mathbb {P}(E)$ be the projectivization of a holomorphic vector bundle $E$ over a compact complex curve $C$. We characterize the existence of an extremal Kähler metric on $\mathbb {P}(E)$ in terms of relative K-polystability and the fact that $E$ decomposes as a direct sum of stable bundles.

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