On surjective morphisms to abelian varieties and a generalization of the Iitaka conjecture
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911964368732160 |
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| author | Meng, Fanjun |
| author_facet | Meng, Fanjun |
| contents | We explore the relationship between fibrations arising naturally from a surjective morphism to an abelian variety. These fibrations encode geometric information about the morphism. Our study focuses on the interplay of these fibrations and presents several applications. Then we propose a generalization of the Iitaka conjecture which predicts an equality of Kodaira dimension of fibrations, and prove it when the base is a smooth projective variety of maximal Albanese dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_01326 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On surjective morphisms to abelian varieties and a generalization of the Iitaka conjecture Meng, Fanjun Algebraic Geometry 14D06, 14K05 We explore the relationship between fibrations arising naturally from a surjective morphism to an abelian variety. These fibrations encode geometric information about the morphism. Our study focuses on the interplay of these fibrations and presents several applications. Then we propose a generalization of the Iitaka conjecture which predicts an equality of Kodaira dimension of fibrations, and prove it when the base is a smooth projective variety of maximal Albanese dimension. |
| title | On surjective morphisms to abelian varieties and a generalization of the Iitaka conjecture |
| topic | Algebraic Geometry 14D06, 14K05 |
| url | https://arxiv.org/abs/2306.01326 |