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In this work we introduce the notion of a pre-weighted homogeneus germ and we show that they are G-finite for G = A and K. We obtain results on the equisingularity of families of hipersurfaces defined by such germs as a consequence of a caracterization of the polihedron of Equisingularity of an analitic germ with isolated singularity. We also show that the gradient polihedron defined by E. Yoshinaga [Y], the filtration conditions defined by J.Damon and T. Gaffney [D G], and the algebraic approach of integral closure of ideais considered by Teissier [T1],[T2] lead to the same convex subset of the polihedron of equisingularity. A partial extension of the above results for complete intersection with isolated singularity is obtained.
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