A K\"ummer construction for Chern-Ricci flat balanced manifolds

TL;DR

This paper develops a gluing construction to produce Chern-Ricci flat balanced metrics on crepant resolutions of non-Kähler Calabi-Yau orbifolds with isolated singularities, advancing solutions to complex geometric systems.

Contribution

It introduces a novel method to extend Chern-Ricci flat balanced metrics from orbifolds to their crepant resolutions using a gluing technique.

Findings

All crepant resolutions of the orbifold admit such metrics.

Application to the Hull-Strominger system solutions.

Extension to singular threefolds with double points.

Abstract

Given a non-K\"ahler Calabi-Yau orbifold with a finite family of isolated singularities endowed with a Chern-Ricci flat balanced metric, we show, via a gluing construction, that all its crepant resolutions admit Chern-Ricci flat balanced metrics, and discuss applications to the search of solutions for the Hull-Strominger system. We also describe the scenario of singular threefolds with ordinary double points, and see that similarly is possible to obtain balanced approximately Chern-Ricci flat metrics.