A Kümmer construction for Chern-Ricci flat balanced manifolds
arXiv:2309.12909
Abstract
Given a non-Kähler 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.
30 pages. Improved presentation and Remark 4.8 added, proof of Lemma 2.7 fixed. Accepted for publication on Math. Z. arXiv admin note: substantial text overlap with arXiv:2301.11636