Genus 3 curves with many involutions and application to maximal curves in characteristic 2
| dc.creator | Nart, Enric | |
| dc.creator | Ritzenthaler, Christophe | |
| dc.date | 2009-05-05 | |
| dc.date.accessioned | 2026-07-07T13:11:50Z | |
| dc.date.available | 2026-07-07T13:11:50Z | |
| dc.description | Let k=F_q be a finite field of characteristic 2. A genus 3 curve C/k has many involutions if the group of k-automorphisms admits a C_2\times C_2 subgroup H (not containing the hyperelliptic involution if C is hyperelliptic). Then C is an Artin-Schreier cover of the three elliptic curves obtained as the quotient of C by the nontrivial involutions of H, and the Jacobian of C is k-isogenous to the product of these three elliptic curves. In this paper we exhibit explicit models for genus 3 curves with many involutions, and we compute explicit equations for the elliptic quotients. We then characterize when a triple (E_1,E_2,E_3) of elliptic curves admits an Artin-Schreier cover by a genus 3 curve, and we apply this result to the construction of maximal curves. As a consequence, when q is nonsquare and m=\lfloor 2 sqrt(q) \rfloor = 1,5,7 mod 8, we obtain that N_q(3)=1+q+3m. We also show that this occurs for an infinite number of values of q nonsquare. | |
| dc.description | 18 pages | |
| dc.identifier | https://arxiv.org/abs/0905.0546 | |
| dc.identifier | http://arxiv.org/abs/0905.0546 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/229409 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 11G20, 14H25 | |
| dc.title | Genus 3 curves with many involutions and application to maximal curves in characteristic 2 | |
| dc.type | text |