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arXiv · 2306.01326

On surjective morphisms to abelian varieties and a generalization of the Iitaka conjecture

Fanjun Meng
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Abstract

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.

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Fanjun Meng. 2023-06-02. On surjective morphisms to abelian varieties and a generalization of the Iitaka conjecture. https://doi.org/10.1007/s00209-024-03505-9

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