Chern-Ricci flat balanced metrics on small resolutions of Calabi-Yau threefolds

TL;DR

This paper demonstrates that small resolutions of certain Calabi-Yau threefolds admit Chern-Ricci flat balanced metrics, providing solutions to equations relevant in string theory compactifications.

Contribution

It introduces a gluing construction proving the existence of Chern-Ricci flat balanced metrics on small resolutions of Calabi-Yau threefolds, including non-K"ahler cases.

Findings

All small resolutions admit Chern-Ricci flat balanced metrics.

These metrics solve the dilatino equation in the Hull-Strominger system.

The construction applies to possibly non-K"ahler resolutions.

Abstract

Given a (smoothable) projective nodal K\"ahler Calabi-Yau threefold, we show, via a gluing construction, that all its - possibly non-K\"ahler - small resolutions admit Chern-Ricci flat balanced metrics, which among other things solve the dilatino equation appearing in the Hull-Strominger system.