Summary
LetR be a Cohen-Macaulay ring andI an unmixed ideal of heightg which is generically a complete intersection and satisfiesI (n)=In for alln≥1. Under what conditions will the Rees algebra be Cohen-Macaulay or have good depth? A series of partial answers to this question is given, relating the Serre condition (S r ) of the associated graded ring to the depth of the Rees algebra. A useful device in arguments of this nature is the canonical module of the Rees algebra. By making use of the technique of the fundamental divisor, it is shown that the canonical module has the expected form: ω R[It] ≅(t(1−t)g−2).
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The third author was partially supported by the NSF
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Morey, S., Noh, S. & Vasconcelos, W.V. Symbolic powers, Serre conditions and Cohen-Macaulay Rees algebras. Manuscripta Math 86, 113–124 (1995). https://doi.org/10.1007/BF02567981
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DOI: https://doi.org/10.1007/BF02567981