Slope instability of projective spaces blown up along a line |
| |
| Authors: | Yoshinori Hashimoto |
| |
| Institution: | 1.Department of Mathematics,University College London,London,UK;2.Aix Marseille Université, CNRS, Centrale Marseille, Institut de Mathématiques de Marseille, UMR 7373,Marseille,France |
| |
| Abstract: | Let \(\text {Bl}_{\mathbb {P}^1} \mathbb {P}^n\) be a Kähler manifold obtained by blowing up a complex projective space \(\mathbb {P}^n\) along a line \(\mathbb {P}^1\). We prove that \(\text {Bl}_{\mathbb {P}^1} \mathbb {P}^n\) is slope unstable with respect to any polarisation, and hence, it does not admit constant scalar curvature Kähler metrics in any rational Kähler class. |
| |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ |
|
