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, $\nu _p \left( {{d \mathord{\left/ {\vphantom {d {d_r }}} \right. \kern-\nulldelimiterspace} {d_r }}} \right) \geqslant \frac{{2n + 1}} {{2\left( {p - 1} \right)}} + 1$\nu _p \left( {{d \mathord{\left/ {\vphantom {d {d_r }}} \right. \kern-\nulldelimiterspace} {d_r }}} \right) \geqslant \frac{{2n + 1}} {{2\left( {p - 1} \right)}} + 1 for all primes p with p(p − 1) ≤ n + 1, where ν _p (d/d _r ) satisfies ${d \mathord{\left/ {\vphantom {d {d_r }}} \right. \kern-\nulldelimiterspace} {d_r }} = \prod\nolimits_{p prime} p ^{\nu _p \left( {{d \mathord{\left/ {\vphantom {d {d_r }}} \right. \kern-\nulldelimiterspace} {d_r }}} \right)}${d \mathord{\left/ {\vphantom {d {d_r }}} \right. \kern-\nulldelimiterspace} {d_r }} = \prod\nolimits_{p prime} p ^{\nu _p \left( {{d \mathord{\left/ {\vphantom {d {d_r }}} \right. \kern-\nulldelimiterspace} {d_r }}} \right)}.