Scalar curvature bounds and tangent cones for Kähler--Ricci shrinkers

Abstract: We prove a uniform scalar curvature bound, depending only on the dimension, for Kähler--Ricci shrinkers. We also prove that every noncompact Kähler--Ricci shrinker has a unique tangent cone at infinity, naturally homeomorphic to the base of its polarized Fano fibration.