Degenerations of Cn and Calabi–Yau metrics

Abstract

We construct infinitely many complete Calabi–Yau metrics on ${\mathbf{C}}^n$ for $n\ge 3$, with maximal volume growth and singular tangent cones at infinity. In addition, we construct Calabi–Yau metrics in neighborhoods of certain isolated singularities whose tangent cones have singular cross section, generalizing work of Hein and Naber.