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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the discriminant of a hyperelliptic curve


Author: P. Lockhart
Journal: Trans. Amer. Math. Soc. 342 (1994), 729-752
MSC: Primary 11G30; Secondary 14H45
MathSciNet review: 1195511
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Abstract | References | Similar Articles | Additional Information

Abstract: The minimal discriminant of a hyperelliptic curve is defined and used to generalize much of the arithmetic theory of elliptic curves. Over number fields this leads to a higher genus version of Szpiro's Conjecture. Analytically, the discriminant is shown to be related to Siegel modular forms of higher degree.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1994-1195511-X
PII: S 0002-9947(1994)1195511-X
Keywords: Hyperelliptic, discriminant
Article copyright: © Copyright 1994 American Mathematical Society