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The Moduli Space of (1,11)-Polarized Abelian Surfaces is Unirational

Published online by Cambridge University Press:  04 December 2007

Mark Gross  and
Sorin Popescu
Mark Gross
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, U.K. E-mail: mgross@maths.warwick.ac.uk
Sorin Popescu
Affiliation:
Department of Mathematics, Columbia University, New York, NY 10027, U.S.A. E-mail: psorin@math.columbia.edu
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Abstract

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We prove that the moduli space $\cal A$11lev of <$>(1,11)-polarized Abelian surfaces with level structure of canonical type is birational to Klein's cubic hypersurface in P4. Therefore, $\cal A$11lev is unirational but not rational, and there are no Γ11-cusp forms of weight 3. The same methods also provide an easy proof of the rationality of $\cal A$9lev.

Keywords

Abelian surfacesmoduliKleine's cubic hypersurface
Type
Research Article
Information
Compositio Mathematica , Volume 126 , Issue 1 , March 2001 , pp. 1 - 24
Copyright
© 2001 Kluwer Academic Publishers