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

Finn Bartsch

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arXiv · 2502.09414

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

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 $\Delta$ on $A$ is finite. To do so, we study the geometry of the scheme $\underline{\mathrm{Hom}}^{\mathrm{nc}}(C, (A, \Delta))$ parametrizing such morphisms from a smooth curve $C$ and show that it admits a quasi-finite non-dominant morphism to $A$.

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Finn Bartsch. 2025-02-13. On the finiteness of maps into simple abelian varieties satisfying certain tangency conditions. https://arxiv.org/abs/2502.09414

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