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- W2949649232 abstract "Abstract Let <?CDATA $K$?> be an algebraically closed field of characteristic different from <?CDATA $2$?> , <?CDATA $g$?> a positive integer, <?CDATA $f(x)$?> a polynomial of degree <?CDATA $2g+1$?> with coefficients in <?CDATA $K$?> and without multiple roots, <?CDATA $mathcal{C}colon y^2=f(x)$?> the corresponding hyperelliptic curve of genus <?CDATA $g$?> over <?CDATA $K$?> , and <?CDATA $J$?> its Jacobian. We identify <?CDATA $mathcal{C}$?> with the image of its canonical embedding in <?CDATA $J$?> (the infinite point of <?CDATA $mathcal{C}$?> goes to the identity element of <?CDATA $J$?> ). It is well known that for every <?CDATA $mathfrak{b} in J(K)$?> there are exactly <?CDATA $2^{2g}$?> elements <?CDATA $mathfrak{a}in J(K)$?> such that <?CDATA $2mathfrak{a}=mathfrak{b}$?> . Stoll constructed an algorithm that provides the Mumford representations of all such <?CDATA $mathfrak{a}$?> in terms of the Mumford representation of <?CDATA $mathfrak{b}$?> . The aim of this paper is to give explicit formulae for the Mumford representations of all such <?CDATA $mathfrak{a}$?> in terms of the coordinates <?CDATA $a,b$?> , where <?CDATA $mathfrak{b}in J(K)$?> is given by a point <?CDATA $P=(a,b) in mathcal{C}(K)subset J(K)$?> . We also prove that if <?CDATA $g>1$?> , then <?CDATA $mathcal{C}(K)$?> does not contain torsion points of orders between <?CDATA $3$?> and <?CDATA $2g$?> ." @default.
- W2949649232 created "2019-06-27" @default.
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- W2949649232 date "2019-06-01" @default.
- W2949649232 modified "2023-10-18" @default.
- W2949649232 title "Division by on odd-degree hyperelliptic curves and their Jacobians" @default.
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- W2949649232 doi "https://doi.org/10.1070/im8773" @default.
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