Non-hyperelliptic curves of genus three over finite fields of characteristic two

Enric Nart, Christophe Ritzenthaler

Research output: Contribution to journalArticleResearchpeer-review

5 Citations (Scopus)

Abstract

Let k 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 models and 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 M3nh of the moduli space of curves of genus M3. By adding to these computations the results of Oort [Moduli of abelian varieties and Newton polygons, C.R. Acad. Sci. Paris 312 (1991) 385-389] and Nart and Sadornil [Hyperelliptic curves of genus three over finite fields of characteristic two, Finite Fields Appl. 10 (2004) 198-200] on the hyperelliptic locus we obtain a complete picture of these strata for M3. © 2005 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)443-473
JournalJournal of Number Theory
Volume116
DOIs
Publication statusPublished - 1 Feb 2006

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