Diffeomorphism classification of smooth weighted complete intersections

Xn(d1, ..., dr−1, dr; w) and Xn(e1, ..., er−1, dr; w) are two complex odd-dimensional smooth weighted complete intersections defined in a smooth weighted hypersurface Xn+r−1(dr; 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 = (ω0, ..., ωn+r) are pairwise relatively prime and odd, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu _p \left( {{d \mathord{\left/ {\vphantom {d {d_r }}} \right. \kern-\nulldelimiterspace} {d_r }}} \right) \geqslant \frac{{2n + 1}} {{2\left( {p - 1} \right)}} + 1$$\end{document} for all primes p with p(p − 1) ≤ n + 1, where νp(d/dr) satisfies \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${d \mathord{\left/ {\vphantom {d {d_r }}} \right. \kern-\nulldelimiterspace} {d_r }} = \prod\nolimits_{p prime} p ^{\nu _p \left( {{d \mathord{\left/ {\vphantom {d {d_r }}} \right. \kern-\nulldelimiterspace} {d_r }}} \right)}$$\end{document}.