Two basic invariants of a complex analytic isolated complete intersection singularity (X, x) are its Milnor number g(X, x) and its Tjurina number z(X, x). The former is the n th Betti number (minus one if n = 0) of a no nsingular nearby fibre, whereas the latter is the dimension of the base space of a miniversal deformation of (X, x). It is conjectured that for n > 1 we always have p(X, x) > z(X, x). So far this has been verified in the following cases: (1) if (X, x) is a hypersurface singularity, (2) if n = 1, (3) if the link of x in X is a rational homology sphere, (4) if (X, x) is quasi-homogeneous [then we actually have equality of p(X, x) and z(X, x)], (5) if n=2 . The first case is rather trivial, the next three are all due to Greuel [3] and the fifth case is due to the first author [4]. Subsequently, J. Wahl expressed for n = 2 the difference of Milnor number and Tjurina number as a sum of non-negative !nvariants of the germ (X, x) [7]. The purpose of this note is to prove the conjecture ~n general. In fact, we obtain a higher dimensional generalization of Wahl's result:
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