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- W2017162564 abstract "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 m R [ I t ] in the Rees algebra R [ I t ] . In the previous work of Huneke, Sally and the authors, the structure of R [ I t ] / P is considered in the case where the residue field R / m = k is relatively algebraically closed in the residue field k v of V . In this paper we consider the structure of R [ I t ] / 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 [ I t ] / P to be normal; we determine the multiplicity of R [ I t ] / P ; we examine the Cohen–Macaulay property of R [ I t ] / P ; and we describe implications for affine components of the blowup of I ." @default.
- W2017162564 created "2016-06-24" @default.
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- W2017162564 date "2013-03-01" @default.
- W2017162564 modified "2023-09-29" @default.
- W2017162564 title "Complete ideals and multiplicities in two-dimensional regular local rings" @default.
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- W2017162564 doi "https://doi.org/10.1016/j.jalgebra.2012.11.014" @default.
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