A K\"ummer construction for Chern-Ricci flat balanced manifolds
Differential Geometry
2024-08-30 v3
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.
Cite
@article{arxiv.2309.12909,
title = {A K\"ummer construction for Chern-Ricci flat balanced manifolds},
author = {Federico Giusti and Cristiano Spotti},
journal= {arXiv preprint arXiv:2309.12909},
year = {2024}
}
Comments
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