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arXiv · 1701.08507

Relative K-polystability of projective bundles over a curve

Vestislav Apostolov·Julien Keller
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Abstract

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

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Vestislav Apostolov, Julien Keller. 2017-01-30. Relative K-polystability of projective bundles over a curve. https://arxiv.org/abs/1701.08507

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