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Effective resolution of cusps on Hilbert modular varieties

Published online by Cambridge University Press:  24 October 2008

G. K. Sankaran
G. K. Sankaran
Affiliation:
Department of Pure Mathematics, University of Cambridge
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Extract

In this paper, we use the Shintani decomposition, known to number theorists, to describe an effective method of finding a resolution of the cusps of a Hilbert modular variety, in any dimension.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 99 , Issue 1 , January 1986 , pp. 51 - 57
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

REFERENCES

[1]Danilov, V. I.. The geometry of toric varieties. Russian Math. Surveys 33 (1978), 97–154.CrossRefGoogle Scholar
[2]Ehlers, F.. Eine Klasse komplexer Mannigfaltigkeiten und die Auflösung einiger isolierter Singularitäten. Math. Ann. 218 (1975), 127–156.Google Scholar
[3]Hirzebruch, F. and van der Geer, G.. Lectures on Hilbert Modular Surfaces (Les Presses del'université de Montréal, 1981).Google Scholar
[4]Shintani, T.. On evaluation of zeta functions of totally real algebraic number fields at non-positive integers. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 23 (1976), 393–417.Google Scholar
[5]Shintani, T.. A remark on zeta functions of algebraic number fields. In Automorphic Forms, Representation Theory and Arithmetic: Papers Presented at the Bombay Colloquium 1979 (Springer-Verlag, 1981), 255–260.Google Scholar
[6]Thomas, E. and Vasquez, A.. On the resolution of cusp singularities and the Shintani decomposition in totally real cubic number fields. Math. Ann. 247 (1980), 1–20.CrossRefGoogle Scholar
[7]Tsuchihashi, H.. Higher-dimensional analogues of periodic continued fractions and cusp singularities. Tohoku Math. J. (2) 35 (1983), 607–639.CrossRefGoogle Scholar