Non hyperelliptic curves of genus three over finite fields of characteristic two
| dc.creator | Nart, Enric | |
| dc.creator | Ritzenthaler, Christophe | |
| dc.date | 2003-12-18 | |
| dc.date | 2004-02-02 | |
| dc.date.accessioned | 2026-07-07T05:04:03Z | |
| dc.date.available | 2026-07-07T05:04:03Z | |
| dc.description | Let k=F_q be a finite field of even characteristic. We obtain in this paper a complete classification, up to k-isomorphism, of non singular quartic plane curves defined over k. We find explicit rational normal models and we give closed formulas for the total number of k-isomorphism classes. We deduce from these computations the number of k-rational points of the different strata by the Newton polygon of the non hyperelliptic locus M_3^{nh} of the moduli space M_3 of curves of genus 3. By adding to these computations the knowed results on the hyperelliptic locus we obtain a complete picture of these strata for M_3. | |
| dc.description | 31 pages ; added references ; the analysis of the supersingular locus has been modified | |
| dc.identifier | https://arxiv.org/abs/math/0312366 | |
| dc.identifier | http://arxiv.org/abs/math/0312366 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69652 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 11G20;14Q05;14H10;14H37 | |
| dc.title | Non hyperelliptic curves of genus three over finite fields of characteristic two | |
| dc.type | text |