On the finiteness of maps into simple abelian varieties satisfying certain tangency conditions
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866929714142117888 |
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| author | Bartsch, Finn |
| author_facet | Bartsch, Finn |
| contents | 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 $\underline{\mathrm{Hom}}^{\mathrm{nc}}(C, (A, Δ))$ parametrizing such morphisms from a smooth curve $C$ and show that it admits a quasi-finite non-dominant morphism to $A$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_09414 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the finiteness of maps into simple abelian varieties satisfying certain tangency conditions Bartsch, Finn Algebraic Geometry Number Theory 14K15 (Primary) 11G35, 14G25 (Secondary) 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 $\underline{\mathrm{Hom}}^{\mathrm{nc}}(C, (A, Δ))$ parametrizing such morphisms from a smooth curve $C$ and show that it admits a quasi-finite non-dominant morphism to $A$. |
| title | On the finiteness of maps into simple abelian varieties satisfying certain tangency conditions |
| topic | Algebraic Geometry Number Theory 14K15 (Primary) 11G35, 14G25 (Secondary) |
| url | https://arxiv.org/abs/2502.09414 |