The moduli space of (1,11)-polarized abelian surfaces is unirational
Algebraic Geometry
2007-05-23 v1
Abstract
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}.
Cite
@article{arxiv.math/9902017,
title = {The moduli space of (1,11)-polarized abelian surfaces is unirational},
author = {Mark Gross and Sorin Popescu},
journal= {arXiv preprint arXiv:math/9902017},
year = {2007}
}
Comments
27 pages, TeX with diagrams.tex. Related Macaulay2 code and PostScript file available at http://www.math.columbia.edu/~psorin/