We consider Fano manifolds admitting an algebraic torus action with general orbit of codimension . Using a recent result of Datar and Székelyhidi, we effectively determine the existence of Kähler–Ricci solitons for those manifolds via the notion of equivariant K-stability. This allows us to give new examples of Kähler–Einstein Fano threefolds and Fano threefolds admitting a nontrivial Kähler–Ricci soliton.
Nathan Ilten. Hendrik Süß. "K-stability for Fano manifolds with torus action of complexity ." Duke Math. J. 166 (1) 177 - 204, 15 January 2017. https://doi.org/10.1215/00127094-3714864