关于无常变体的投射态以及饭高猜想的一般化

IF 1 3区数学 Q1 MATHEMATICS

Mathematische Zeitschrift Pub Date : 2024-05-09 DOI:10.1007/s00209-024-03505-9

Fanjun Meng

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引用次数: 0

摘要

我们探讨了由无方变的投射态自然产生的纤点之间的关系。这些纤点编码了关于态的几何信息。我们的研究侧重于这些纤维的相互作用，并提出了一些应用。然后，我们提出了饭高猜想的广义化，该猜想预言了纤维的小平维度相等，并证明了当基底是最大阿班维度的光滑投影变时，小平维度相等。

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

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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