A generalization of Ross-Thomas' slope theory
14L24, 14J17, 32Q15 | Mathematics - Algebraic Geometry | Mathematics - Differential Geometry
arxiv: Mathematics::Differential Geometry | Mathematics::Symplectic Geometry
We give a formula of the Donaldson-Futaki invariants for certain type of semi test configurations, which essentially generalizes Ross-Thomas' slope theory. The positivity (resp. non-negativity) of those "a priori special" Donaldson-Futaki invariants implies K-stability (resp. K-semistability). We show its applicability by proving K-(semi)stability of certain polarized varieties with semi-log-canonical singularities, generalizing some results by Ross-Thomas.