Slope instability of projective spaces blown up along a line

Yoshinori Hashimoto (1, 2)

1 I2M - Institut de Mathématiques de Marseille
2 UCL London - Department of Mathematics

Let be a Kahler manifold obtained by blowing up a complex projective space along a line . We prove that is slope unstable with respect to any polarisation, and hence, it does not admit constant scalar curvature Kahler metrics in any rational Kahler class.

Mots clés: Slope stability; K-stability; Constant scalar curvature Kahler metrics; Extremal Kahler metrics

Domaines: Variables complexes [math.CV]; Analyse fonctionnelle [math.FA]

Yoshinori Hashimoto. Slope instability of projective spaces blown up along a line. Annals of Global Analysis and Geometry, 2018, 53 (2), pp.251-264. ⟨10.1007/s10455-017-9576-y⟩. ⟨hal-02051730⟩