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On bounding the Stückrad-Vogel multiplicity

Published online by Cambridge University Press:  20 January 2009

L. O'Carroll
L. O'Carroll
Affiliation:
Department of MathematicsUniversity of EdinburghJames Clerk Maxwell Building Mayfield Road Edinburgh EH9 3JZ
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Using a classical result of Nagata, Achilles, Huneke and Vogel gave a criterion for the Stückrad-Vogel multiplicity to take the value one. We use Huneke's extension of Nagata's theorem to give a necessary condition for the Stückrad-Vogel multiplicity to have an arbitrary preassigned bound, under certain conditions. A usable criterion of multiplicity n results (given mild hypotheses). We also revisit some basic results in the Stückrad-Vogel theory in the light of the behaviour of tensor products of affine primary rings, and also revisit some arguments of Achilles, Huneke and Vogel from the point of view of fibre rings.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 34 , Issue 2 , June 1991 , pp. 251 - 257
Copyright
Copyright © Edinburgh Mathematical Society 1991

References

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