A Remark on Fujino's work on the canonical bundle formula via period maps
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929337991692288 |
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| author | Kim, Hyunsuk |
| author_facet | Kim, Hyunsuk |
| contents | Fujino gave a proof in [Fuj03] for the semi-ampleness of the moduli part in the canonical bundle formula in the case when the general fibers are K3 surfaces or Abelian varieties. We show a similar statement when the general fibers are primitive symplectic varieties with mild singularities. This answers a question of Fujino raised in the same article. Moreover, using the structure theory of varieties with trivial first Chern class, we reduce the question of semi-ampleness in the case of families of K-trivial varieties to a question when the general fibers satisfy a slightly weaker Calabi-Yau condition. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_05489 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Remark on Fujino's work on the canonical bundle formula via period maps Kim, Hyunsuk Algebraic Geometry 14C30, 14D07, 14E30, 14J27 Fujino gave a proof in [Fuj03] for the semi-ampleness of the moduli part in the canonical bundle formula in the case when the general fibers are K3 surfaces or Abelian varieties. We show a similar statement when the general fibers are primitive symplectic varieties with mild singularities. This answers a question of Fujino raised in the same article. Moreover, using the structure theory of varieties with trivial first Chern class, we reduce the question of semi-ampleness in the case of families of K-trivial varieties to a question when the general fibers satisfy a slightly weaker Calabi-Yau condition. |
| title | A Remark on Fujino's work on the canonical bundle formula via period maps |
| topic | Algebraic Geometry 14C30, 14D07, 14E30, 14J27 |
| url | https://arxiv.org/abs/2405.05489 |