Unobstructed deformations for singular Calabi-Yau varieties
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914328067702784 |
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| author | Friedman, Robert |
| author_facet | Friedman, Robert |
| contents | Let $Y$ be a compact Gorenstein analytic space with only isolated singularities and trivial dualizing sheaf. A recent paper of Imagi studies the deformation theory of $Y$ in case the singularities of $Y$ are weighted homogeneous and rational and $Y$ is Kähler. In this note, assuming that $H^1(Y;\mathcal{O}_Y) =0$, we generalize Imagi's results to the case where the singularities of $Y$ are Du Bois, with no assumption that they be weighted homogeneous, and where the Kähler assumption is replaced by the hypothesis that there is a resolution of singularities of $Y$ satisfying the $\partial\bar\partial$-lemma. As a consequence, if the singularities of $Y$ are additionally local complete intersections, then the deformations of $Y$ are unobstructed. The log Calabi-Yau and Fano cases are also discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_09857 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unobstructed deformations for singular Calabi-Yau varieties Friedman, Robert Algebraic Geometry 14J32 (Primary) 14D15, 32G05 (Secondary) Let $Y$ be a compact Gorenstein analytic space with only isolated singularities and trivial dualizing sheaf. A recent paper of Imagi studies the deformation theory of $Y$ in case the singularities of $Y$ are weighted homogeneous and rational and $Y$ is Kähler. In this note, assuming that $H^1(Y;\mathcal{O}_Y) =0$, we generalize Imagi's results to the case where the singularities of $Y$ are Du Bois, with no assumption that they be weighted homogeneous, and where the Kähler assumption is replaced by the hypothesis that there is a resolution of singularities of $Y$ satisfying the $\partial\bar\partial$-lemma. As a consequence, if the singularities of $Y$ are additionally local complete intersections, then the deformations of $Y$ are unobstructed. The log Calabi-Yau and Fano cases are also discussed. |
| title | Unobstructed deformations for singular Calabi-Yau varieties |
| topic | Algebraic Geometry 14J32 (Primary) 14D15, 32G05 (Secondary) |
| url | https://arxiv.org/abs/2506.09857 |