Remarks on contact structures and vector fields on isolated complete intersection singularities
| dc.creator | Seade, Jose | |
| dc.date | 2006-09-15 | |
| dc.date.accessioned | 2026-07-07T07:24:52Z | |
| dc.date.available | 2026-07-07T07:24:52Z | |
| dc.description | 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 $μ(X,0) \equiv (-1)^{n-1}$ 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. | |
| dc.identifier | https://arxiv.org/abs/math/0609448 | |
| dc.identifier | http://arxiv.org/abs/math/0609448 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/116534 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Algebraic Topology | |
| dc.subject | 53Dxx, 32Sxx | |
| dc.title | Remarks on contact structures and vector fields on isolated complete intersection singularities | |
| dc.type | text |