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Stable quintuples and terminal quotient singularities

Published online by Cambridge University Press:  24 October 2008

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

We shall prove below part of a conjecture made by Shigefumi Mori, David Morrison and Ian Morrison in the course of their investigations into the properties of isolated terminal cyclic quotient singularities of prime Gorenstein index in dimension four [1]. The reader of the present paper need have no knowledge of algebraic geometry, because we quickly reduce the problem to one about the geometry of numbers that can be solved by elementary calculations. The calculations are very lengthy and not quite routine, so what the reader does need is either patience, if he intends to check them, or faith, if he does not. We give only part of the calculations below. Full details may be obtained from the author.*

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 107 , Issue 1 , January 1990 , pp. 91 - 101
Copyright
Copyright © Cambridge Philosophical Society 1990

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References

REFERENCES

[1]Mori, S., Morrison, D. R. and Morrison, I.. On four-dimensional terminal singularities. Math. Comp. 51 (1988), 769–786.CrossRefGoogle Scholar
[2]Reid, M.. Minimal models of canonical 3-folds. In Algebraic Varieties and Analytic Varieties, Advanced Studies in Pure Mathematics 1 (ed. Iitaka, S.) (Kinokuniya and North-Holland, 1983), pp. 395–418.Google Scholar
[3]Wilson, P. M. H.. Towards birational classification of algebraic varieties. Bull. London Math. Soc. 19 (1987), 1–48.CrossRefGoogle Scholar