Diffeomorphism classification of smooth weighted complete intersections

X n (d1, ..., dr.1, d r ; w) and X n (e1, ..., er.1, d r ; w) are two complex odd-dimensional smooth weighted complete intersections defined in a smooth weighted hypersurface Xn+r.1(d r ; w). We prove that they are diffeomorphic if and only if they have the same total degree d, the Pontrjagin classes and the Euler characteristic, under the following assumptions: the weights w = (.0, ..., .n+r) are pairwise relatively prime and odd, .p(d/dr).2n+12(p.1)+1 for all primes p with p(p . 1) . n + 1, where . p (d/d r ) satisfies d/dr=.pprimep.p(d/dr)