| Résume | It was recently shown by Chen-Sun-Wang that the Kähler-Ricci flow on a Fano manifold gives rise to a certain algebraic degeneration of the manifold. They conjectured that this degeneration should be ”most destabilising”. We introduce a new stability notion, with respect to which the Chen-Sun-Wang degeneration is most destabilising. As an application, we prove a general convergence result for the Kähler-Ricci flow on Fano manifolds admitting a Kähler-Ricci soliton, generalising work of Tian-Zhu and Tian-Zhang-Zhu. This is joint work with Gabor Székelyhidi. |
