{"language":[{"iso":"eng"}],"type":"preprint","date_updated":"2025-01-15T11:35:48Z","author":[{"last_name":"Seguin","id":"102487","first_name":"Beranger Fabrice","full_name":"Seguin, Beranger Fabrice"}],"user_id":"102487","citation":{"short":"B.F. Seguin, ArXiv:2409.18246 (2024).","ieee":"B. F. Seguin, “Counting Components of Hurwitz Spaces,” <i>arXiv:2409.18246</i>. 2024.","mla":"Seguin, Beranger Fabrice. “Counting Components of Hurwitz Spaces.” <i>ArXiv:2409.18246</i>, 2024.","ama":"Seguin BF. Counting Components of Hurwitz Spaces. <i>arXiv:240918246</i>. Published online 2024.","chicago":"Seguin, Beranger Fabrice. “Counting Components of Hurwitz Spaces.” <i>ArXiv:2409.18246</i>, 2024.","apa":"Seguin, B. F. (2024). Counting Components of Hurwitz Spaces. In <i>arXiv:2409.18246</i>.","bibtex":"@article{Seguin_2024, title={Counting Components of Hurwitz Spaces}, journal={arXiv:2409.18246}, author={Seguin, Beranger Fabrice}, year={2024} }"},"external_id":{"arxiv":["2409.18246"]},"status":"public","title":"Counting Components of Hurwitz Spaces","year":"2024","abstract":[{"text":"For a finite group $G$, we describe the asymptotic growth of the number of\r\nconnected components of Hurwitz spaces of marked $G$-covers (of both the affine\r\nand projective lines) whose monodromy classes are constrained in a certain way,\r\nas the number of branch points grows to infinity. More precisely, we compute\r\nboth the exponent and (in many cases) the coefficient of the leading monomial\r\nin the count of components containing covers whose monodromy group is a given\r\nsubgroup of $G$. By the work of Ellenberg, Tran, Venkatesh and Westerland, this\r\nasymptotic behavior is related to the distribution of field extensions\r\nof~$\\mathbb{F}_q(T)$ with Galois group $G$.","lang":"eng"}],"date_created":"2025-01-15T11:24:56Z","publication":"arXiv:2409.18246","_id":"58186"}