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1 results

  • Cohen–Macaulay Multi–Rees Algebras

  • Eero Hyry
  • Journal:
    Compositio Mathematica / Volume 130 / Issue 3 / February 2002
    Published online by Cambridge University Press:
    04 December 2007, pp. 319-343
    Print publication:
    February 2002
    • Article
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  • Let A be a local ring, and let I1,…,Ir ⊂ A be ideals of positive height. In this article we compare the Cohen–Macaulay property of the multi–Rees algebra RA(I1,…,Ir) to that of the usual Rees algebra RA(I1 ··· Ir) of the product I1 ··· Ir. In particular, when the analytic spread of I1 ··· Ir is small, this leads to necessary and sufficient conditions for the Cohen–Macaulayness of RA(I1,…,Ir). We apply our results to the theory of joint reductions and mixed multiplicities.