تقرير
Finite translation orbits on double families of abelian varieties
| العنوان: | Finite translation orbits on double families of abelian varieties |
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| المؤلفون: | Dolce, Paolo, Tropeano, Francesco |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory, Mathematics - Algebraic Geometry, 14Gxx, 14Kxx |
| الوصف: | Consider two families of $g$-dimensional abelian varieties induced by two distinct rational maps on the same variety $\overline{\mathcal A}$ onto two bases $\overline S_1$ and $\overline S_2$ and having big common domain of definition. Two non-torsion sections of these families induce two (birational) fiberwise translations on $\overline{\mathcal A}$, respectively. We show that if $\dim \overline S_1+\dim \overline S_2\le 2g$, the points with finite orbit under the action of a certain subset of the group generated by both translations lie in a proper Zariski closed subset that can be described to a certain extent. Our work is a higher dimensional generalization of a result of Corvaja, Tsimermann and Zannier. Comment: 22 pages, 2 figures. Changes in Proposition 1.7 and Proposition 2.1. Comments are welcome |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2401.07015 |
| رقم الأكسشن: | edsarx.2401.07015 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |