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Intersection theory in an equicharacteristic regular local ring and the relative intersection theory


Author: James Hornell
Journal: Proc. Amer. Math. Soc. 36 (1972), 8-12
MSC: Primary 14A25; Secondary 13H15
DOI: https://doi.org/10.1090/S0002-9939-1972-0309936-6
MathSciNet review: 0309936
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Abstract: Using the intersection theory of the notes of Serre, Algèbre locale. Multiplicités, the valuation theoretic formula for a hypersurface is given, and it is shown that transversality is equivalent to intersection multiplicity one. The intersection multiplicity of Algèbre locale. Multiplicités is computed for two algebraic varieties over an arbitrary field and compared to the intersection number of Weil's Foundations of algebraic geometry.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0309936-6
Keywords: Relative intersection theory, intersection theory, equicharacteristic regular local ring, transversality, intersection multiplicity one
Article copyright: © Copyright 1972 American Mathematical Society

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