The moduli space of (111)-polarized abelian surfaces is unirational

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Gross, M. W. ; Popescu, Sorin (2001)
  • Publisher: Cambridge University Press
  • Related identifiers: doi: 10.1023/A:1017518027822
  • Subject: QA
    arxiv: Mathematics::Algebraic Geometry | Physics::History of Physics | Quantitative Biology::Cell Behavior

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.
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