Uniqueness of shrinking gradient Kähler–Ricci solitons on non-compact toric manifolds

We show that, up to biholomorphism, there is at most one complete (Formula presented.) -invariant shrinking gradient Kähler–Ricci soliton on a non-compact toric manifold M. We also establish uniqueness without assuming (Formula presented.) -invariance if the Ricci curvature is bounded and if the soliton vector field lies in the Lie algebra (Formula presented.) of (Formula presented.). As an application, we show that, up to isometry, the unique complete shrinking gradient Kähler–Ricci soliton with bounded scalar curvature on (Formula presented.) is the standard product metric associated to the Fubini–Study metric on (Formula presented.) and the Euclidean metric on (Formula presented.).