# A generalization of Ross-Thomas' slope theory

Research paper by Yuji Odaka

Indexed on: 15 Apr '11Published on: 15 Apr '11Published in: Mathematics - Algebraic Geometry

#### Abstract

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.