Computing the arithmetic genus of Hilbert modular fourfolds
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- by H. G. Grundman and L. E. Lippincott;
- Math. Comp. 75 (2006), 1553-1560
- DOI: https://doi.org/10.1090/S0025-5718-06-01842-4
- Published electronically: March 21, 2006
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Abstract:
The Hilbert modular fourfold determined by the totally real quartic number field $k$ is a desingularization of a natural compactification of the quotient space $\Gamma _k \backslash {\mathcal H}^4$, where $\Gamma _k=\mbox {PSL}_2({\mathcal O}_k)$ acts on ${\mathcal H}^4$ by fractional linear transformations via the four embeddings of $k$ into $\bf R$. The arithmetic genus, equal to one plus the dimension of the space of Hilbert modular cusp forms of weight $(2,2,2,2)$, is a birational invariant useful in the classification of these varieties. In this work, we describe an algorithm allowing for the automated computation of the arithmetic genus and give sample results.References
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Bibliographic Information
- H. G. Grundman
- Affiliation: Bryn Mawr College, 101 N. Merion Ave., Bryn Mawr, Pennsylvania 19010
- MR Author ID: 307385
- Email: grundman@brynmawr.edu
- L. E. Lippincott
- Affiliation: Bryn Mawr College, 101 N. Merion Ave., Bryn Mawr, Pennsylvania 19010
- Email: llippinc@brynmawr.edu
- Received by editor(s): April 23, 2004
- Received by editor(s) in revised form: May 10, 2005
- Published electronically: March 21, 2006
- Additional Notes: The first author wishes to acknowledge the support of the Faculty Research Fund of Bryn Mawr College.
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 75 (2006), 1553-1560
- MSC (2000): Primary 11F41, 14E08; Secondary 14J10, 14J35
- DOI: https://doi.org/10.1090/S0025-5718-06-01842-4
- MathSciNet review: 2219045