  This article is concerned with an observation for proving non-existence of
canonical Kahler metrics. The idea is to use a rather explicit type of
degeneration that applies in many situations. Namely, in a variation on a theme
introduced by Ross-Thomas, we consider flops of the deformation to the normal
cone. This yields a rather widely applicable notion of stability that is still
completely explicit and readily computable, but with wider scope. We describe
some applications, among them, a proof of one direction of the Calabi
conjecture for asymptotically logarithmic del Pezzo surfaces.

Algebraic Geometry;Differential Geometry