G. La Nave

Singularities and K-semistability

In this paper we extend the notion of Futaki invariant to big and nef classes in such a way that it defines a continuous function on the \K\ cone up to the boundary. We apply this concept to prove that reduced normal crossing singularities are sufficient to check $K$-semistability. A similar improvement on Donaldson's lower bound for Calabi energy is given.