# Compactification of certain K\"ahler manifolds with nonnegative Ricci curvature

## TL;DR

This paper proves compactification theorems for certain complete K"ahler manifolds with nonnegative Ricci curvature, showing their relation to algebraic varieties and metric tangent cones at infinity.

## Contribution

It establishes that specific noncompact K"ahler Ricci flat manifolds are crepant resolutions of affine varieties and describes their degeneration to tangent cones.

## Key findings

- Complete noncompact K"ahler Ricci flat manifolds with maximal volume growth are crepant resolutions.
- Such manifolds degenerate to a unique metric tangent cone at infinity.
- The results connect geometric analysis with algebraic geometry.

## Abstract

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