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Non-splitting of prime divisors

Published online by Cambridge University Press:  24 October 2008

Judith D. Sally
Judith D. Sally
Affiliation:
Department of Mathematics, Northwestern University, U.S.A.
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Extract

In this study of complete, or integrally closed, ideals in a two-dimensional regular local ring (R, m), Zariski established a one-to-one correspondence between prime divisors of R, i.e. rank 1 discrete valuations v birationally dominating R with residue field of transcendence degree 1 over R/m, and m-primary simple complete ideals Iv in R; cf. [17] and [18]. In this correspondence, the blow-up of such an ideal has unique exceptional prime and the localization at this prime is the valuation ring of a prime divisor of R. In this paper, we will study such ideals in a more general setting, so we begin by recalling some definitions and background results.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 103 , Issue 2 , March 1988 , pp. 251 - 256
Copyright
Copyright © Cambridge Philosophical Society 1988

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References

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