| Abstract: | ABSTRACT Let X = Spec(R) be a reduced equidimensional algebraic variety over an algebraically closed field k. Let Y = Spec(R/𝔮) be a codimension one ordinary multiple subvariety, where 𝔮 is a prime ideal of height 1 of R. If U is a nonempty open subset of Y and 𝔪 a closed point of U, we denote by A ? R 𝔪 its local ring in X, by 𝔭 the extension of 𝔮 in A, and by K the algebraic closure of the residue field k(𝔭). Then there exists a bijection γ𝔪:Proj(G 𝔭(A) ? A/𝔭 k) → Proj(G(A 𝔭) ? k(𝔭)K) such that for every subset Σ of Proj(G 𝔭(A) ? A/𝔭 k), the Hilbert function of Σ coincides with the Hilbert function of γ𝔪(Σ). We examine some applications. We study the structure of the tangent cone at a closed point of a codimension one ordinary multiple subvariety. |
