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 Kähler 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 the Calabi energy is given.
Singularities and K-semistability / C. Arezzo; A. Della Vedova; G. La Nave. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - 2012:4(2012), pp. 849-869. [10.1093/imrn/rnr044]