The moduli space of (1,11)-polarized abelian surfaces is unirational

الأصل · EN

We prove that the moduli space A₁₁lev of (1,11) polarized abelian surfaces with level structure of canonical type is birational to Klein's cubic hypersurface: a²b+b²c+c²d+d²e+e²a=0 in P⁴. Therefore, A₁₁lev is unirational but not rational, and there are no Gamma₁₁-cusp forms of weight 3. The same methods also provide an easy proof of the rationality of A₉lev.