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Extra info for Algebra Lineal OEA 5

Example text

SNOUSSI 2 We start by giving simple models for normal quasi-ordinary singularities: We prove that they are all normalization of some simple singularities that we determine from the group of the unramified covering they induce outside the coordinate hyperplanes. 4]). As a corollary we prove that any local quasi-ordinary morphism of Cn is equivalent to a morphism of the form (x1 , . . , xn ) → (xa1 1 , . . , xann ), for some positive integers a1 , . . , an . We study the case of finite cyclic quotient singularities, and give examples of normal quasi-ordinary singularities that are neither finite cyclic quotient nor minimal.

4], P. Popescu-Pampu gave an other proof for the same result, and as he says, his proof extends to general normal quasiordinary singularities. We give here a “hand-made” proof of that theorem. Let Γ be a subgroup of Zn of finite index. 1. If we call v1 , . . , vn the rows of the matrix M −1 , then (det M )vi is the ith row of the adjoint matrix Adj M . Recall that XAdj M,det M is an irreducible component of the space defined by the ideal of C[X1 , . . , Xn , Z1 , . . ,an ) = X1a1 · · · Xnan .

Massey – Trends in equisingularity theory, in Singularity theory, Liverpool 1996, London Math. Soc. , vol. 263, Cambridge Univ. Press, 1999, p. 207–248. [GS] G. Gonzalez-Sprinberg – Cycle maximal et invariant d’Euler local des singularit´es isol´ees de surfaces, Topology 21 (1982), no. 4, p. 401–408. T. – Sur un crit`ere d’´equisingularit´e, C. R. Acad. Sci. Paris S´er. I Math. 272 (1971), p. 138–140. [LJ] M. , K. Saito & B. ), World Scientific, 1995, p. 345–369. [LJ-Te] M. Lejeune-Jalabert & B.