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DEFORMATIONS WITH CONSTANT MILNOR NUMBER AND MULTIPLICITY OF COMPLEX HYPERSURFACES The first named author is partially supported by CNPq-Grant 30055692-6.
We investigate the constancy of the Milnor number of one parameter deformations of holomorphic germs of functions . As a consequence of these results we give a positive answer to Zariski's question for Milnor constant families satisfying a non-degeneracy condition on the Jacobian ideals.