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The quadric threefold cone of S4

Published online by Cambridge University Press:  26 February 2010

J. E. Reeve  and
J. A. Tyrrell
J. E. Reeve
Affiliation:
King's College, London, W.C.2.
J. A. Tyrrell
Affiliation:
King's College, London, W.C.2.
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Extract

In a recent paper [1], we have given some account of theories of equivalence and intersection on a singular algebraic surface and have shown that such theories share many of the simple properties enjoyed by corresponding theories on non-singular surfaces. Another paper [2], now in preparation, will extend this work to singular varieties of arbitrary dimension. In the meantime, Zobel [3] has drawn attention to some suspect arguments of Samuel [4] concerning the specialization of intersections on a singular variety.

Type
Research Article
Information
Mathematika , Volume 8 , Issue 2 , December 1961 , pp. 87 - 98
Copyright
Copyright © University College London 1961

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References

1. Reeve, J. E. and Tyrrell, J. A., “Intersection theory on a singular algebraic surface”, Proc. London Math. Soc. (in course of publication).Google Scholar
2. Reeve, J. E. and Tyrrell, J. A., “Intersection theory on a singular algebraic variety” (in preparation).Google Scholar
3. Zobel, A., “On the non-specialisation of intersections on a singular variety”, Mathematika, 8 (1961), 39–44.CrossRefGoogle Scholar
4. Samuel, P., “La notion de multiplicité en Algèbre et en Géométrie Algébrique”, J. de Math. (9), 30 (1951), 159–274.Google Scholar
5. Segre, B., “Variazione continua ed omotopia in geometria algebrica”, Annali di Mat. (4), 50 (1960), 149–186.Google Scholar