Asymptotically conical Calabi-Yau metrics with cone singularities along a compact divisor

Abstract

AbstractWe construct Asymptotically Locally Euclidean (ALE) and, more generally, asymptotically conical Calabi–Yau metrics with cone singularities along a compact simple normal crossing divisor. In particular, this includes the case of the minimal resolution of 2D quotient singularities for any finite subgroup $\Gamma \subset U(2)$ acting freely on the three-sphere, hence generalizing Kronheimer’s construction of smooth ALE gravitational instantons.