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The moduli space of (111)-polarized abelian surfaces is unirational
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Gross, M. W. and Popescu, Sorin (2001) The moduli space of (111)-polarized abelian surfaces is unirational. Compositio Mathematica, Vol.12 (No.1). pp. 1-24. doi:10.1023/A:1017518027822 ISSN 0010-437X.
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Official URL: http://dx.doi.org/10.1023/A:1017518027822
Abstract
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.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Abelian varieties, Hypersurfaces, Moduli theory, Functions of several complex variables, Geometry, Algebraic | ||||
Journal or Publication Title: | Compositio Mathematica | ||||
Publisher: | Cambridge University Press | ||||
ISSN: | 0010-437X | ||||
Official Date: | March 2001 | ||||
Dates: |
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Volume: | Vol.12 | ||||
Number: | No.1 | ||||
Page Range: | pp. 1-24 | ||||
DOI: | 10.1023/A:1017518027822 | ||||
Status: | Peer Reviewed | ||||
Access rights to Published version: | Open Access (Creative Commons) |
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