Hyperelliptic curves of genus three over finite fields of even characteristic

Enric Nart; Daniel Sadornil

doi:https://doi.org/10.1016/j.ffa.2003.08.002

Hyperelliptic curves of genus three over finite fields of even characteristic

Enric Nart, Daniel Sadornil

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

8 Citations (Scopus)

Abstract

In this paper we classify hyperelliptic curves of genus 3 defined over a finite field k of even characteristic. We consider rational models representing all k-isomorphy classes of curves with a given arithmetic structure for the ramification divisor and we find necessary and sufficient conditions for two models of the same type to be k-isomorphic. Also, we compute the automorphism group of each curve and an explicit formula for the total number of curves. © 2003 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	198-220
Journal	Finite Fields and Their Applications
Volume	10
DOIs	https://doi.org/10.1016/j.ffa.2003.08.002
Publication status	Published - 1 Jan 2004

Keywords

Automorphism group
Hyperelliptic curves
Moduli spaces

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https://doi.org/10.1016/j.ffa.2003.08.002

Cite this

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abstract = "In this paper we classify hyperelliptic curves of genus 3 defined over a finite field k of even characteristic. We consider rational models representing all k-isomorphy classes of curves with a given arithmetic structure for the ramification divisor and we find necessary and sufficient conditions for two models of the same type to be k-isomorphic. Also, we compute the automorphism group of each curve and an explicit formula for the total number of curves. {\textcopyright} 2003 Elsevier Inc. All rights reserved.",

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AU - Sadornil, Daniel

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N2 - In this paper we classify hyperelliptic curves of genus 3 defined over a finite field k of even characteristic. We consider rational models representing all k-isomorphy classes of curves with a given arithmetic structure for the ramification divisor and we find necessary and sufficient conditions for two models of the same type to be k-isomorphic. Also, we compute the automorphism group of each curve and an explicit formula for the total number of curves. © 2003 Elsevier Inc. All rights reserved.

AB - In this paper we classify hyperelliptic curves of genus 3 defined over a finite field k of even characteristic. We consider rational models representing all k-isomorphy classes of curves with a given arithmetic structure for the ramification divisor and we find necessary and sufficient conditions for two models of the same type to be k-isomorphic. Also, we compute the automorphism group of each curve and an explicit formula for the total number of curves. © 2003 Elsevier Inc. All rights reserved.

KW - Automorphism group

KW - Hyperelliptic curves

KW - Moduli spaces

U2 - https://doi.org/10.1016/j.ffa.2003.08.002

DO - https://doi.org/10.1016/j.ffa.2003.08.002

M3 - Article

SN - 1071-5797

VL - 10

SP - 198

EP - 220

JO - Finite Fields and Their Applications

JF - Finite Fields and Their Applications

ER -

Hyperelliptic curves of genus three over finite fields of even characteristic

Abstract

Keywords

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