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

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• 作者：Reynald Lercier^a ; ^b ; ¹ ; ^{reynald.lercier@m4x.org} ; Christophe Ritzenthaler^c ; ¹ ; ^{ritzenth@iml.univ-mrs.fr}
• 关键词：14Q05 ; 13A50 ; 14H10 ; 14H37
• 刊名：Journal of Algebra
• 出版年：2012
• 出版时间：15 December, 2012
• 年：2012
• 卷：372
• 期：Complete
• 页码：595-636
• 全文大小：510 K

文摘

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.