【摘要】
It was conjectured by Székelyhidi that a polarized manifold admits an extremal Kähler metric in the polarization class if and only if it is relatively K-polystable. In addition, a well-known folklore conjecture asserts that every toric Fano manifold admits an extremal Kähler metric in its first Chern class. Applying relative K-unstability criterion to a specific toric Fano manifold, we show that there exists a 10-dimensional toric Fano manifold that does not admit an extremal Kähler metric. This talk is based on joint work with D. S. Hwang and H. Sato.
