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The moduli space of (1,11)-polarized abelian surfaces is unirational
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The moduli space of (1,11)-polarized abelian surfaces is unirational
classification
math.AG
keywords
abelianmodulipolarizedspacesurfacesunirationalbirationalcanonical
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We prove that the moduli space A_{11}^{lev} of (1,11) polarized abelian surfaces with level structure of canonical type is birational to Klein's cubic hypersurface: a^2b+b^2c+c^2d+d^2e+e^2a=0 in P^4. Therefore, A_{11}^{lev} is unirational but not rational, and there are no Gamma_{11}-cusp forms of weight 3. The same methods also provide an easy proof of the rationality of A_{9}^{lev}.
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