Abstract
We consider the problem of finding an upper bound for the possible torsion of a divisor on a curve of genus 2, when everything is defined over an algebraic number field. Mainly, we show how to write the equation of the Kummer surface of the Jacobian of a curve of genus 2 in terms of the equation of the curve. This allows one to calculate a bound on the torsion which seems better than the bound derived from Riemann-Weil theory. Finally, we discuss briefly a different approach which is valid for all hy — perelliptic curves, at the cost of a considerable increase in complexity.
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Bibliography
F. Baldassari and B. Dwork. "On second order linear differential equations with algebraic solution". In Contributions to Algebraic Geometry, Johns Hopkins Press, Baltimore 1979.
J.H. Davenport. On the Integration of Algebraic Functions. Lecture Notes in Computer Science 102, Springer 1981.
F. Enriques. Lezioni sulla teoria delle superficie algebriche, Parte I (Raccolte da L. Campadelli). Padova 1932.
F. Klein. Gesammelte Mathematische Abhandlungen. Vol. 1. Berlin, Springer Verlag 1973.
E. Kummer Collected Papers. Berlin, Springer Verlag 1975.
R. Risch. "The Solution of the problem of integration in finite terms". Bull. A.M.S. 76 (1970) 605–608.
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© 1984 Springer-Verlag Berlin Heidelberg
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Berry, T.G. (1984). Detecting torsion divisors on curves of genus 2. In: Fitch, J. (eds) EUROSAM 84. EUROSAM 1984. Lecture Notes in Computer Science, vol 174. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0032835
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DOI: https://doi.org/10.1007/BFb0032835
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-13350-6
Online ISBN: 978-3-540-38893-7
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