Complete ideals and multiplicities in two-dimensional regular local rings

JOURNAL OF ALGEBRA

卷:377

Article

Heinzer, William¹  Kim, Mee-Kyoung² 

[1] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

[2] Sungkyunkwan Univ, Dept Math, Suwon 440746, South Korea

关键词: Rees valuation;    Complete ideal;    Regular ring;    Normal domain;    Local quadratic transform;    Proper transform;    Minimal multiplicity;   

DOI  :  10.1016/j.jalgebra.2012.11.014

来源: Elsevier

【 摘 要 】

Let I be a complete m-primary ideal of a two-dimensional regular local ring (R, m). The beautiful theory developed by Zariski about complete ideals of R implies that the Rees valuation rings V of I are in a natural one-to-one correspondence with the minimal primes P of the ideal mR[It] in the Rees algebra R[It]. In the previous work of Huneke, Sally and the authors, the structure of R[It]/P is considered in the case where the residue field R/m = k is relatively algebraically closed in the residue field k, of V. In this paper we consider the structure of R[It]/P without the assumption that k is relatively algebraically closed in k(v) and obtain the following results: we give necessary and sufficient conditions for R[It]/P to be normal; we determine the multiplicity of R[It]/P; we examine the Cohen-Macaulay property of R[It]/P; and we describe implications for affine components of the blowup of I. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

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