Counting hyperelliptic curves

Enric Nart

doi:10.1016/j.aim.2009.01.001

Counting hyperelliptic curves

Enric Nart

Department of Mathematics

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

6 Citations (Scopus)

Abstract

We find a closed formula for the number hyp (g) of hyperelliptic curves of genus g over a finite field k = Fq of odd characteristic. These numbers hyp (g) are expressed as a polynomial in q with integer coefficients that depend on g and the set of divisors of q - 1 and q + 1. As a by-product we obtain a closed formula for the number of self-dual curves of genus g. A hyperelliptic curve is defined to be self-dual if it is k-isomorphic to its own hyperelliptic twist. © 2009 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	774-787
Journal	Advances in Mathematics
Volume	221
DOIs	https://doi.org/10.1016/j.aim.2009.01.001
Publication status	Published - 20 Jun 2009

Keywords

Finite field
Hyperelliptic curve
Self-dual curve

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10.1016/j.aim.2009.01.001

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AB - We find a closed formula for the number hyp (g) of hyperelliptic curves of genus g over a finite field k = Fq of odd characteristic. These numbers hyp (g) are expressed as a polynomial in q with integer coefficients that depend on g and the set of divisors of q - 1 and q + 1. As a by-product we obtain a closed formula for the number of self-dual curves of genus g. A hyperelliptic curve is defined to be self-dual if it is k-isomorphic to its own hyperelliptic twist. © 2009 Elsevier Inc. All rights reserved.

KW - Finite field

KW - Hyperelliptic curve

KW - Self-dual curve

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VL - 221

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EP - 787

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Counting hyperelliptic curves

Abstract

Keywords

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