English

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.

Keywords

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

R2 v1 2026-06-28T12:29:31.859Z