Deforming Calabi-Yau Threefolds
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
1995
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| _version_ | 1866916998629294080 |
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| author | Gross, Mark |
| author_facet | Gross, Mark |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_alg_geom_9506022 |
| institution | arXiv |
| publishDate | 1995 |
| record_format | arxiv |
| spellingShingle | Deforming Calabi-Yau Threefolds Gross, Mark Algebraic Geometry 14J32 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. |
| title | Deforming Calabi-Yau Threefolds |
| topic | Algebraic Geometry 14J32 |
| url | https://arxiv.org/abs/alg-geom/9506022 |