Deformations of fibered Calabi--Yau varieties
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arXiv
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| Auteurs principaux: | , , , , , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917410801451008 |
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| author | Bakker, Benjamin DeVleming, Kristin Filipazzi, Stefano Laza, Radu Li, Jennifer Svaldi, Roberto Wang, Chengxi Zhao, Junyan |
| author_facet | Bakker, Benjamin DeVleming, Kristin Filipazzi, Stefano Laza, Radu Li, Jennifer Svaldi, Roberto Wang, Chengxi Zhao, Junyan |
| contents | Kollár showed that small deformations of elliptically fibered smooth $K$-torsion varieties with $H^2(X,\mathcal{O}_X)=0$ remain elliptically fibered. We extend this result to any fibered smooth $K$-torsion variety $X$ with $H^2(X,\mathcal{O}_X)=0$, using Hodge theoretic techniques and the $T^1$-lifting criterion of Kawamata--Ran. More generally, our strategy implies that even without the cohomological assumption, small deformations of a semiample line bundle on a smooth $K$-torsion variety remain semiample up to homological equivalence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_14024 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Deformations of fibered Calabi--Yau varieties Bakker, Benjamin DeVleming, Kristin Filipazzi, Stefano Laza, Radu Li, Jennifer Svaldi, Roberto Wang, Chengxi Zhao, Junyan Algebraic Geometry High Energy Physics - Theory Differential Geometry Primary: 14D15, 14J32, Secondary: 14D07 Kollár showed that small deformations of elliptically fibered smooth $K$-torsion varieties with $H^2(X,\mathcal{O}_X)=0$ remain elliptically fibered. We extend this result to any fibered smooth $K$-torsion variety $X$ with $H^2(X,\mathcal{O}_X)=0$, using Hodge theoretic techniques and the $T^1$-lifting criterion of Kawamata--Ran. More generally, our strategy implies that even without the cohomological assumption, small deformations of a semiample line bundle on a smooth $K$-torsion variety remain semiample up to homological equivalence. |
| title | Deformations of fibered Calabi--Yau varieties |
| topic | Algebraic Geometry High Energy Physics - Theory Differential Geometry Primary: 14D15, 14J32, Secondary: 14D07 |
| url | https://arxiv.org/abs/2604.14024 |