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

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

1999-02-02

arxiv.org/abs/math/9902017v1

Mathematics

Algebraic Geometry

27 pages, TeX with diagrams.tex. Related Macaulay2 code and PostScript file available at http://www.math.columbia.edu/~psorin/

Scientific paper

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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