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Number of generators of a Cohen–Macaulay ideal

✍ Scribed by Hans Schoutens

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
88 KB
Volume
259
Category
Article
ISSN
0021-8693

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✦ Synopsis

For a Noetherian local ring R, if R/a is Cohen-Macaulay, then the ideal a can be generated by at most (e -2)(νd -1) + 2 elements, where ν is the embedding dimension of R and where d and e 3 are the dimension and the multiplicity of R/a, respectively. This bound is in general much sharper than the bounds given by Sally or Boratyński-Eisenbud-Rees in case a has height bigger than 2. Moreover, no Cohen-Macaulay assumption on R is required.

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