Humbert surfaces and the Kummer plane
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- by Christina Birkenhake and Hannes Wilhelm PDF
- Trans. Amer. Math. Soc. 355 (2003), 1819-1841 Request permission
Abstract:
A Humbert surface is a hypersurface of the moduli space $\mathcal A_2$ of principally polarized abelian surfaces defined by an equation of the form $az_1+bz_2+cz_3+d(z_2^2-z_1z_3)+e=0$ with integers $a,\ldots ,e$. We give geometric characterizations of such Humbert surfaces in terms of the presence of certain curves on the associated Kummer plane. Intriguingly this shows that a certain plane configuration of lines and curves already carries all information about principally polarized abelian surfaces admitting a symmetric endomorphism with given discriminant.References
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Additional Information
- Christina Birkenhake
- Affiliation: Christina Birkenhake, Universität Mainz, Staudingerweg 9, D-55099 Mainz, Germany
- Email: birken@Mathematik.uni-mainz.de
- Hannes Wilhelm
- Affiliation: Hannes Wilhelm, 10 Studley Count, 4 Jamestown Way, London E14 2DA, England
- Email: Hannes.Wilhelm@dresdner-bank.com
- Received by editor(s): February 11, 2002
- Published electronically: January 8, 2003
- Additional Notes: Supported by DFG-contracts Bi 448/4-1 and Hu 337/5-1
- © Copyright 2003 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 355 (2003), 1819-1841
- MSC (2000): Primary 14K10; Secondary 14H50
- DOI: https://doi.org/10.1090/S0002-9947-03-03238-0
- MathSciNet review: 1953527