About canonical Kähler metrics on Mumford semistable projective bundles over a curve

Julien Keller (1)

1 I2M - Institut de Mathématiques de Marseille

We study the existence of canonical K\"ahler metrics on the projectivisation of strictly Mumford semistable holomorphic vector bundles over a complex curve. We also provide an algebro-geometric characterization of these metrics.

Mots clés: conic singularity; K-stability; vector bundle; Chow stability; stability; projective bundles; ruled manifold; balanced; Kahler metric

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

Julien Keller. About canonical Kähler metrics on Mumford semistable projective bundles over a curve. Journal of the London Mathematical Society, 2016, 93 (1), pp.159-174. ⟨10.1112/jlms/jdv066⟩. ⟨hal-01282553⟩