Relative K-polystability of projective bundles over a curve

Vestislav Apostolov (1) , Julien Keller (2)

1 CIRGET - Centre interuniversitaire de recherches en géométrie et topologie [Montréal]
2 I2M - Institut de Mathématiques de Marseille

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.

Domaines: Géométrie algébrique [math.AG]; Variables complexes [math.CV]; Géométrie différentielle [math.DG]

Vestislav Apostolov, Julien Keller. Relative K-polystability of projective bundles over a curve. Trans. Amer. Math. Soc., 2019, 372 (1), pp.233-266. ⟨hal-01481897⟩