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- W1644492029 abstract "Let $(X,0)$ be an isolated complete intersection complex singularity ($X$ can also be smooth at 0). Let $K$ be its link, $cal X$ its canonical contact structure and $D_X$ the complex vector bundle associated to $cal X$. We prove that the bundle $D_X$ is trivial if and only if the Milnor number of $X$ satisfies $mu(X,0) equiv (-1)^{n-1}$ modulo $(n-1)!$. This follows from a general theorem stating that the complex orthogonal complement of a vector field in $X$ with an isolated singularity at 0 is trivial iff the GSV-index of $v$ is a multiple of $(n-1)!$. We have also an application to foliation theory: a holomorphic foliation $cal F$ in a ball $B_r$ around the origin in $C^3$, with an isolated singularity at 0, admits a $C^infty$ normal section (away from 0) iff its multiplicity (or local index) is even, and this happens iff its normal bundle in $B_r setminus {0}$ is topologically trivial." @default.
- W1644492029 created "2016-06-24" @default.
- W1644492029 creator A5037740636 @default.
- W1644492029 date "2008-01-01" @default.
- W1644492029 modified "2023-09-27" @default.
- W1644492029 title "Remarks on contact structures and vector fields on isolated complete intersection singularities" @default.
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- W1644492029 doi "https://doi.org/10.1090/conm/459/08971" @default.
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