From Calabi's extremal metrics to scalar-flat Kähler cones

Vestislav Apostolov, Abdellah Lahdili, Chung-Ming Pan

We prove that for any smooth polarized complex $n$-dimensional manifold $(X,L_X)$ which admits an extremal Kähler metric in $c_1(L_X)$, and for any integer $k$ large enough (in te…