LAUSR

We show that a Kähler-Ricci soliton on a Fano manifold can always be smoothly approximated by a sequence of relative anticanonically balanced metrics, also called quantized Kähler-Ricci solitons. The proof uses an equivariant version of Berezin-Toeplitz quantization to extend a strategy due to Donaldson, and can be seen as the quantization of a method due to Tian and Zhu, using quantized Futaki invariants as obstructions for quantized Kähler-Ricci solitons. As a by-product, we show that a KählerEinstein Fano manifold does not necessarily admit anticanonically balanced metrics in the usual sense when its automorphism group is not discrete.