文摘
Let X be a Fano manifold. We say that a hermitian metric \(\phi \) on \(-K_X\) with positive curvature \(\omega _{\phi }\) is a K?hler–Ricci soliton if it satisfies the equation \(\mathrm{Ric}(\omega _{\phi }) - \omega _{\phi } = L_{V_{KS}} \omega _{\phi }\) 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 K?hler–Ricci solitons attached to the sequence \(\{V_k\}\). Keywords Fano manifold K?hler–Ricci soliton Balanced metric