Publication
For a given K-polystable Fano variety X and a natural number l such that (X, 1/l B) is log canonical for some B ∈ | − lKX|, we show that there exists a rational number 0 < c1 < 1 depending only on X and l, such that D ∈ | − lKX| is GIT-(semi/poly)stable under the action of Aut(X) if and only if the log pair (X, ϵ/l D) is K-(semi/poly)stable for any rational 0 < ϵ < c1