About the equivalence of divisor classes on hyperelliptic curves and a quotient of linear forms by an algebraic group action

2006/04/26 by Víctor Neumann, Neumann, Victor Gonzalo Lopez
Computer Science · Mathematics · #11G30 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Cryptography and Residue Arithmetic #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.math/0604545

openalex publication_date 2006/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a hyperelliptic curve of genus g, a divisor in general position of degree g+1 is given by polynomial equations. There is an action from an algebraic group on the representations of divisors by polynomials which fixes divisor classes. This structure reduces the question of rationality of divisor classes to rationality of polynomials which is more easy to control.

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