On surjective morphisms to abelian varieties and a generalization of the Iitaka conjecture
arXiv:2306.01326 · doi:10.1007/s00209-024-03505-9
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.
28 pages; v2: minor changes; final version. arXiv admin note: text overlap with arXiv:2207.08359