Compactification of certain Kähler manifolds with nonnegative Ricci curvature

We prove compactification theorems for some complete Kähler manifolds with nonnegative Ricci curvature. Among other things, we prove that a complete non-compact Ricci-flat Kähler manifold with maximal volume growth and quadratic curvature decay is a crepant resolution of a normal affine algebraic variety. Furthermore, such an affine variety degenerates in two steps to the unique metric tangent cone at infinity.