Minimisation of 2-coverings of genus 2 Jacobians
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Peer-reviewed
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Abstract
Abstract An important problem in computational arithmetic geometry is to find changes of coordinates to simplify a system of polynomial equations with rational coefficients. This is tackled by a combination of two techniques, called minimisation and reduction. We give an algorithm for minimising certain pairs of quadratic forms, subject to the constraint that the first quadratic form is fixed. This has applications to 2-descent on the Jacobian of a genus 2 curve.
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Acknowledgements: This work originated as a summer project carried out by the second author and supervised by the first author. We thank the Research in the CMS Programme for their support.
Journal Title
manuscripta mathematica
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0025-2611
1432-1785
1432-1785
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176
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Springer Science and Business Media LLC
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Except where otherwised noted, this item's license is described as http://creativecommons.org/licenses/by/4.0/