Diffeomorphism classification of smooth weighted complete intersections

X _n (d ₁, ..., d _r−1, d _r ; w) and X _n (e ₁, ..., e _r−1, d _r ; w) are two complex odd-dimensional smooth weighted complete intersections defined in a smooth weighted hypersurface X _n+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 = (ω ₀, ..., ω _n+r ) are pairwise relatively prime and odd, $nu _p left( {{d mathord{left/ {vphantom {d {d_r }}} right. kern-nulldelimiterspace} {d_r }}} right) geqslant frac{{2n + 1}} {{2left( {p - 1} right)}} + 1$nu _p left( {{d mathord{left/ {vphantom {d {d_r }}} right. kern-nulldelimiterspace} {d_r }}} right) geqslant frac{{2n + 1}} {{2left( {p - 1} right)}} + 1 for all primes p with p(p − 1) ≤ n + 1, where ν _p (d/d _r ) satisfies ${d mathord{left/ {vphantom {d {d_r }}} right. kern-nulldelimiterspace} {d_r }} = prodnolimits_{p prime} p ^{nu _p left( {{d mathord{left/ {vphantom {d {d_r }}} right. kern-nulldelimiterspace} {d_r }}} right)}${d mathord{left/ {vphantom {d {d_r }}} right. kern-nulldelimiterspace} {d_r }} = prodnolimits_{p prime} p ^{nu _p left( {{d mathord{left/ {vphantom {d {d_r }}} right. kern-nulldelimiterspace} {d_r }}} right)}.