Boundedness of some fibered K-trivial varieties
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913921528496128 |
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| author | Engel, Philip Filipazzi, Stefano Greer, François Mauri, Mirko Svaldi, Roberto |
| author_facet | Engel, Philip Filipazzi, Stefano Greer, François Mauri, Mirko Svaldi, Roberto |
| contents | We prove that irreducible Calabi-Yau varieties of a fixed dimension, admitting a fibration by abelian varieties or primitive symplectic varieties of a fixed analytic deformation class, are birationally bounded. We prove that there are only finitely many deformation classes of primitive symplectic varieties of a fixed dimension, admitting a Lagrangian fibration. We also show that fibered Calabi-Yau 3-folds are bounded. Conditional on the generalized abundance or hyperkähler SYZ conjecture, our results prove that there are only finitely many deformation classes of hyperkähler varieties, of a fixed dimension, with $b_2 \geq 5$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_00973 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Boundedness of some fibered K-trivial varieties Engel, Philip Filipazzi, Stefano Greer, François Mauri, Mirko Svaldi, Roberto Algebraic Geometry High Energy Physics - Theory Differential Geometry 14J27 14J32 14J42 (Primary) 14D06 14E30 14D07 14K05 (Secondary) We prove that irreducible Calabi-Yau varieties of a fixed dimension, admitting a fibration by abelian varieties or primitive symplectic varieties of a fixed analytic deformation class, are birationally bounded. We prove that there are only finitely many deformation classes of primitive symplectic varieties of a fixed dimension, admitting a Lagrangian fibration. We also show that fibered Calabi-Yau 3-folds are bounded. Conditional on the generalized abundance or hyperkähler SYZ conjecture, our results prove that there are only finitely many deformation classes of hyperkähler varieties, of a fixed dimension, with $b_2 \geq 5$. |
| title | Boundedness of some fibered K-trivial varieties |
| topic | Algebraic Geometry High Energy Physics - Theory Differential Geometry 14J27 14J32 14J42 (Primary) 14D06 14E30 14D07 14K05 (Secondary) |
| url | https://arxiv.org/abs/2507.00973 |