Deforming Calabi-Yau Threefolds
Abstract
This paper first generalises the Bogomolov-Tian-Todorov unobstructedness theorem to the case of Calabi-Yau threefolds with canonical singularities. The deformation space of such a Calabi-Yau threefold is no longer smooth, but the general principle is that the obstructions to deforming such a threefold are precisely the obstructions to deforming the singularities of the threefold. Secondly, these results are applied to smoothing singular Calabi-Yau threefolds with crepant resolutions. Any such Calabi-Yau threefold with isolated complete intersection singularities which are not ordinary double points is smoothable. A Calabi-Yau threefold with non-complete intersection isolated singularities is proved to be smoothable under much stronger hypotheses.
Cite
@article{arxiv.alg-geom/9506022,
title = {Deforming Calabi-Yau Threefolds},
author = {Mark Gross},
journal= {arXiv preprint arXiv:alg-geom/9506022},
year = {2025}
}
Comments
Post-publication revision, correcting one error and clarifying an aspect of the proof of Theorem 2.2