Nef cones of fiber products and an application to the Cone Conjecture
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866909124163272704 |
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| author | Gachet, Cécile Lin, Hsueh-Yung Wang, Long |
| author_facet | Gachet, Cécile Lin, Hsueh-Yung Wang, Long |
| contents | We prove a decomposition theorem for the nef cone of smooth fiber products over curves, subject to the necessary condition that their Néron--Severi space decomposes. We apply it to describe the nef cone of so-called Schoen varieties, which are the higher dimensional analogues of the Calabi--Yau threefolds constructed by Schoen. Schoen varieties give rise to Calabi--Yau pairs, and in each dimension at least three, there exist Schoen varieties with non-polyhedral nef cone. We prove the Kawamata--Morrison--Totaro Cone Conjecture for the nef cones of Schoen varieties, which generalizes the work by Grassi and Morrison. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2210_02779 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Nef cones of fiber products and an application to the Cone Conjecture Gachet, Cécile Lin, Hsueh-Yung Wang, Long Algebraic Geometry We prove a decomposition theorem for the nef cone of smooth fiber products over curves, subject to the necessary condition that their Néron--Severi space decomposes. We apply it to describe the nef cone of so-called Schoen varieties, which are the higher dimensional analogues of the Calabi--Yau threefolds constructed by Schoen. Schoen varieties give rise to Calabi--Yau pairs, and in each dimension at least three, there exist Schoen varieties with non-polyhedral nef cone. We prove the Kawamata--Morrison--Totaro Cone Conjecture for the nef cones of Schoen varieties, which generalizes the work by Grassi and Morrison. |
| title | Nef cones of fiber products and an application to the Cone Conjecture |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2210.02779 |