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 corollary, every complete Kähler–Ricci shrinker with quasi-positive Ricci curvature is compact.