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The moduli space of bilevel-6 abelian surfaces

Published online by Cambridge University Press:  22 January 2016

G. K. Sankaran  and
J. G. Spandaw
G. K. Sankaran
Affiliation:
Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, England, gks@maths.bath.ac.uk
J. G. Spandaw
Affiliation:
Institut für Mathematik, Universität Hannover, Postfach 6009, D-30060 Hannover, Germany, spandaw@math.uni-hannover.de
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Abstract

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We show that the moduli space of abelian surfaces with polarisation of type (1,6) and a bilevel structure has positive Kodaira dimension and indeed pg ≥ 3. To do this we show that three of the Siegel cusp forms with character for the paramodular symplectic group constructed by Gritsenko and Nikulin are cusp forms without character for the modular group associated to this moduli problem. We then calculate the divisors of the corresponding differential forms, using information about the fixed loci of elements of the paramodular group previously obtained by Brasch.

Keywords

11F4614K10
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 168 , 2002 , pp. 113 - 125
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2002

References

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