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Jacobian in genus 2

Published online by Cambridge University Press:  24 October 2008

J. W. S. Cassels
J. W. S. Cassels
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, 16 Mill Lane, Cambridge
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Extract

In [2] the author proposed the study of the geometry and arithmetic of the general curve

of genus 2 over a general groundfield such as the rationals in order to attack Diophantine problems. He gave the form of the Jacobian, and Flynn[4, 5] determined the group law on it. This paper is preparatory to a planned study of heights under duality. It extends to a general groundfield the description of the Jacobian as the variety of lines on the intersection of two quadric surfaces in P5 given over the complexes in the last chapter of the textbook [7] of Griffiths and Harris. This description is a generalization of that of a curve of genus 1 as the intersection of two quadric surfaces in P3 and is a special case of a more general result [3]: its first appearances seem to be in [12] and [13].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 114 , Issue 1 , July 1993 , pp. 1 - 8
Copyright
Copyright © Cambridge Philosophical Society 1993

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References

REFERENCES

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