Diffeomorphism classification of smooth weighted complete intersections |
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Authors: | Jian Bo Wang Yu Yu Wang |
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Affiliation: | (1) Department of Mathematics, Tianjin University, Tianjin, 300072, P. R. China;(2) College of Mathematical Science, Tianjin Normal University, Tianjin, 300387, P. R. China |
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Abstract: | 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)}. |
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Keywords: | Weighted projective space weighted complete intersection weighted hypersurface diffeo-morphism classification |
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