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arXiv · 2412.10284

Division polynomials in Mumford coordinates

Julia Bernatska
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Abstract

An effective method of computing division polynomials in terms of Mumford coordinates is presented. As an example, division polynomials for $3$- and $4$-torsion divisors on a genus two curve are obtained explicitly in terms of Mumford coordinates, and $x$-, $y$-coordinates of the support of torsion divisors. As a result, $n$-torsion divisors on a given curve can be computed directly from the division polynomials. Alternatively, these divisors are obtained by solving the Jacobi inversion problem at points of the Jacobian variety of order $n$.

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Julia Bernatska. 2024-12-13. Division polynomials in Mumford coordinates. https://doi.org/10.3233/nicsp250006

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