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Intersection multiplicities and tangent cones

Published online by Cambridge University Press:  24 October 2008

B. R. Tennison
B. R. Tennison
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, Cambridge
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Extract

The following result has at least the appeal of intuitive plausibility. Let U and V be subvarieties of an algebraic variety X; let x ∈ X be an isolated point of the intersection of U and V, and let I(X, U. V, x) denote the intersection multiplicity (in some sense to be made precise) of U and V at x. Now let Tx be the tangent space to X at x, within which lie the tangent cones Cu, Cv to U and V at x. Then

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 85 , Issue 1 , January 1979 , pp. 33 - 42
Copyright
Copyright © Cambridge Philosophical Society 1979

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References

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