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

  • Mark Gross (a1) and Sorin Popescu (a2)

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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Compositio Mathematica
  • ISSN: 0010-437X
  • EISSN: 1570-5846
  • URL: /core/journals/compositio-mathematica
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