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• W2953174328 abstract "Let $(S, mathfrak n) $ be a regular local ring and let $I subseteq mathfrak n^2 $ be a perfect ideal of $S. $ Sharp upper bounds on the minimal number of generators of $I$ are known in terms of the Hilbert function of $R=S/I. $ Starting from information on the ideal $I, $ for instance the minimal number of generators, a difficult task is to find good bounds on the minimal number of generators of the leading ideal $I^* $, which defines the tangent cone of $R$ or to give information on its graded structure. Motivated by papers of S.C. Kothari, S. Goto ${it{et al.}}$ concerning the leading ideal of a complete intersection $I=(f,g) $ in a regular local ring, we present results provided ht$(I)=2.$ If $I$ is a complete intersection, we prove that the Hilbert function of $R$ determines the graded Betti numbers of the leading ideal and, as a consequence, we recover most of the results of the previously quoted papers. The description is more complicated if $nu(I) >2$ and a careful investigation can be provided when $nu(I)=3. $ Several examples illustrating our results are given." @default.
• W2953174328 created "2019-06-27" @default.
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• W2953174328 date "2014-02-12" @default.
• W2953174328 modified "2023-09-27" @default.
• W2953174328 title "The Tangent Cone of a local ring of codimension 2" @default.
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• W2953174328 hasPublicationYear "2014" @default.
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