Asymptotic stability for Kähler–Ricci solitons

Let X be a Fano manifold. We say that a hermitian metric ϕ on -K_X with positive curvature ω_ϕ is a Kähler–Ricci soliton if it satisfies the equation (Formula Presented.) for some holomorphic vector field V_KS. The candidate for a vector field V_KS is uniquely determined by the holomorphic structure of X up to conjugacy, hence depends only on the holomorphic structure of X. We introduce a sequence {V_k} of holomorphic vector fields which approximates V_KS and fits to the quantized settings. Moreover, we also discuss about the existence and convergence of the quantized Kähler–Ricci solitons attached to the sequence {V_k}.