Hyperelliptic curves with extra involutions
| dc.creator | Gutierrez, J. | |
| dc.creator | Shaska, T. | |
| dc.date | 2006-01-18 | |
| dc.date.accessioned | 2026-07-07T06:59:03Z | |
| dc.date.available | 2026-07-07T06:59:03Z | |
| dc.description | The purpose of this paper is to study hyperelliptic curves with extra involutions. The locus $Ł_g$ of such genus $g$ hyperelliptic curves is a $g$-dimensional subvariety of the moduli space of hyperelliptic curves $\H_g$. We discover a birational parametrization of $Ł_g$ via dihedral invariants and show how these invariants can be used to determine the field of moduli of points $\p \in Ł_g$. We conjecture that for $\p\in \H_g$ with $|\Aut(\p)| > 2$ the field of moduli is a field of definition and prove this conjecture for any point $\p\in Ł_g$ such that the Klein 4-group is embedded in the reduced automorphism group of $\p$. Further, for $g=3$ we show that for every moduli point $\p \in \H_3$ such that $| \Aut (\p) | > 4$, the field of moduli is a field of definition and provide a rational model of the curve over its field of moduli. | |
| dc.identifier | https://arxiv.org/abs/math/0601456 | |
| dc.identifier | http://arxiv.org/abs/math/0601456 | |
| dc.identifier | LMS J. of Comp. Math., 8, (2005), 102-115 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/107607 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Group Theory | |
| dc.title | Hyperelliptic curves with extra involutions | |
| dc.type | text |