Shimura curve computations via K3 surfaces of Neron-Severi rank at least 19

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Shimura curve computations via K3 surfaces of Neron-Severi rank at least 19

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Title: Shimura curve computations via K3 surfaces of Neron-Severi rank at least 19
Author: Elkies, Noam
Citation: Elkies, Noam D. 2006. Shimura curves for level-3 subgroups of the (2,3,7) triangle group and some other examples. Lecture Notes in Computer Science (4076): 302-316.
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Abstract: It is known that K3 surfaces S whose Picard number rho (= rank of the Neron-Severi group of S) is at least 19 are parametrized by modular curves X, and these modular curves X include various Shimura modular curves associated with congruence subgroups of quaternion algebras over Q. In a family of such K3 surfaces, a surface has rho=20 if and only if it corresponds to a CM point on X. We use this to compute equations for Shimura curves, natural maps between them, and CM coordinates well beyond what could be done by working with the curves directly as we did in "Shimura Curve Computations" (1998).
Published Version: http://dx.doi.org/10.1007/978-3-540-79456-1_13
Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA
Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:2797445

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  • FAS Scholarly Articles [7078]
    Peer reviewed scholarly articles from the Faculty of Arts and Sciences of Harvard University
 
 

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