On the finiteness of maps into simple abelian varieties satisfying certain tangency conditions

IF 0.9 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2025-06-13 DOI:10.1112/blms.70119

Finn Bartsch

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Abstract

We show that given a simple abelian variety $A$ and a normal variety $V$ defined over a finitely generated field $K$ of characteristic zero, the set of non-constant morphisms $V \to A$ satisfying certain tangency conditions imposed by a Campana orbifold divisor $Δ$ on $A$ is finite. To do so, we study the geometry of the scheme ${\underset{̲}{Hom}}^{nc} (C, (A, Δ))$ parameterizing such morphisms from a smooth curve $C$ and show that it admits a quasi-finite non-dominant morphism to $A$ .

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满足一定相切条件的简单阿贝尔变换映射的有限性

我们证明了给定一个简单的阿贝尔变量a $A$和一个定义在特征为零的有限生成域K $K$上的正常变量V $V$，在A $A$上满足Campana轨道除数Δ $\Delta$所施加的相切条件的非常态射集合V→A $V \rightarrow A$是有限的。为此，我们研究了hom＿no＿nc (C, (A，Δ)) $\underline{\operatorname{Hom}}^{\operatorname{nc}}(C, (A, \Delta))$从光滑曲线C $C$参数化了这样的态射，并表明它承认a $A$的拟有限非显性态射。

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