Kähler-Ricci Shrinkers with Nonnegative Ricci Curvature

We prove that every complete Kähler--Ricci shrinker with nonnegative Ricci curvature is holomorphically isometric to $\mathbb{C}^k\times N^{n-k}$ for some $0\le k\le n$, where $\mathbb{C}^k$ is the Gaussian shrinker and $N$ is a compact Kähler--Ricci shrinker with nonnegative Ricci curvature. As a c