Hyperelliptic curves and their invariants: Geometric, arithmetic and algorithmic aspects

被引：33

作者：

Lercier, Reynald ^{[2
,3
]}

Ritzenthaler, Christophe ^{[1
]}

机构：

[1] CNRS, UMR 6206, Inst Math Luminy, F-13288 Marseille, France

[2] DGA MI, F-35174 La Roche Marguerite, Bruz, France

[3] Univ Rennes 1, Inst Rech Math Rennes, F-35042 Rennes, France

来源：

JOURNAL OF ALGEBRA | 2012年 / 372卷

关键词：

Algorithm; Automorphism; Binary form; Covariant; Field of moduli; Field of definition; Genus; 3; Invariant; Moduli space; Reconstruction; Weighted projective space; MODULI; FIELDS; DEFINITION; GENUS-3; RATIONALITY; NUMBER;

D O I：

10.1016/j.jalgebra.2012.07.054

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We apply classical invariant theory of binary forms to explicitly characterize isomorphism classes of hyperelliptic curves of small genus and, conversely, propose algorithms for reconstructing hyperelliptic models from given invariants. We focus on genus 3 hyperelliptic curves. Both geometric and arithmetic aspects are considered. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：595 / 636

页数：42

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