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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Schottky's form and the hyperelliptic locus


Author: Cris Poor
Journal: Proc. Amer. Math. Soc. 124 (1996), 1987-1991
MSC (1991): Primary 11F46; Secondary 14K25, 11E45
MathSciNet review: 1327038
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Abstract: We show that Schottky's modular form, $J_{g}$, has in every genus an irreducible divisor which contains the hyperelliptic locus. We also improve a corollary of Igusa concerning Siegel modular forms that must necessarily vanish on the hyperelliptic locus.


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Additional Information

Cris Poor
Affiliation: Department of Mathematics, Fordham University, Bronx, New York 10458
Email: poor@murray.fordham.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03312-6
PII: S 0002-9939(96)03312-6
Keywords: Analytic class invariant, theta series, hyperelliptic
Received by editor(s): October 24, 1994
Received by editor(s) in revised form: January 30, 1995
Communicated by: Albert Baernstein II
Article copyright: © Copyright 1996 American Mathematical Society