Plane quartics with Jacobians isomorphic to a hyperelliptic Jacobian
Author:
Everett W. Howe
Journal:
Proc. Amer. Math. Soc. 129 (2001), 16471657
MSC (2000):
Primary 14H40; Secondary 14H45
Published electronically:
November 21, 2000
MathSciNet review:
1814093
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Abstract: We show how for every integer one can explicitly construct distinct plane quartics and one hyperelliptic curve over all of whose Jacobians are isomorphic to one another as abelian varieties without polarization. When we say that the curves can be constructed ``explicitly'', we mean that the coefficients of the defining equations of the curves are simple rational expressions in algebraic numbers in whose minimal polynomials over can be given exactly and whose decimal approximations can be given to as many places as is necessary to distinguish them from their conjugates. We also prove a simplystated theorem that allows one to decide whether or not two plane quartics over , each with a pair of commuting involutions, are isomorphic to one another.
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Additional Information
Everett W. Howe
Affiliation:
Center for Communications Research, 4320 Westerra Court, San Diego, California 921211967
Email:
however@alumni.caltech.edu
DOI:
http://dx.doi.org/10.1090/S0002993900058871
PII:
S 00029939(00)058871
Keywords:
Curve,
Jacobian,
polarization,
Torelli,
quartic
Received by editor(s):
December 1, 1998
Received by editor(s) in revised form:
October 9, 1999
Published electronically:
November 21, 2000
Communicated by:
Ron Donagi
Article copyright:
© Copyright 2000
American Mathematical Society
