{"publication":"arXiv:2303.05903","author":[{"last_name":"Seguin","full_name":"Seguin, Beranger Fabrice","id":"102487","first_name":"Beranger Fabrice"}],"user_id":"102487","title":"Fields of Definition of Components of Hurwitz Spaces","date_created":"2025-01-15T11:24:23Z","external_id":{"arxiv":["2303.05903"]},"citation":{"apa":"Seguin, B. F. (2023). Fields of Definition of Components of Hurwitz Spaces. In <i>arXiv:2303.05903</i>.","short":"B.F. Seguin, ArXiv:2303.05903 (2023).","mla":"Seguin, Beranger Fabrice. “Fields of Definition of Components of Hurwitz Spaces.” <i>ArXiv:2303.05903</i>, 2023.","chicago":"Seguin, Beranger Fabrice. “Fields of Definition of Components of Hurwitz Spaces.” <i>ArXiv:2303.05903</i>, 2023.","bibtex":"@article{Seguin_2023, title={Fields of Definition of Components of Hurwitz Spaces}, journal={arXiv:2303.05903}, author={Seguin, Beranger Fabrice}, year={2023} }","ama":"Seguin BF. Fields of Definition of Components of Hurwitz Spaces. <i>arXiv:230305903</i>. Published online 2023.","ieee":"B. F. Seguin, “Fields of Definition of Components of Hurwitz Spaces,” <i>arXiv:2303.05903</i>. 2023."},"type":"preprint","year":"2023","date_updated":"2025-01-15T11:35:23Z","status":"public","abstract":[{"text":"For a fixed finite group $G$, we study the fields of definition of\r\ngeometrically irreducible components of Hurwitz moduli schemes of marked\r\nbranched $G$-covers of the projective line. The main focus is on determining\r\nwhether components obtained by \"gluing\" two other components, both defined over\r\na number field $K$, are also defined over $K$. The article presents a list of\r\nsituations in which a positive answer is obtained. As an application, when $G$\r\nis a semi-direct product of symmetric groups or the Mathieu group $M_{23}$,\r\ncomponents defined over $\\mathbb{Q}$ of small dimension ($6$ and $4$,\r\nrespectively) are shown to exist.","lang":"eng"}],"_id":"58184","language":[{"iso":"eng"}]}