تقرير
Families of elliptic curves over the four-pointed configuration space and exceptional sequences for the braid group on four strands
| العنوان: | Families of elliptic curves over the four-pointed configuration space and exceptional sequences for the braid group on four strands |
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| المؤلفون: | Chen, William Y., Salter, Nick |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Algebraic Geometry, Mathematics - Geometric Topology |
| الوصف: | We show that the configuration space of four unordered points in $\mathbb{C}$ with barycenter 0 is isomorphic to the space of triples $(E,Q,\omega)$, where $E$ is an elliptic curve, $Q\in E^\circ$ a nonzero point, and $\omega$ a nonzero holomorphic differential on $E$. At the level of fundamental groups, our construction unifies two classical exceptional exact sequences involving the braid group $B_4$: namely, the sequence $1\rightarrow F_2\rightarrow B_4\rightarrow B_3\rightarrow 1$, where $F_2$ is a free group of rank 2, related to Ferrari's solution of the quartic, and the sequence $1\rightarrow \mathbb{Z} \rightarrow B_4\rightarrow\operatorname{Aut}^+(F_2)\rightarrow 1$ of Dyer-Formanek-Grossman. Comment: 7 pages. Comments welcome! |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2402.11081 |
| رقم الأكسشن: | edsarx.2402.11081 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |