Remarks on contact structures and vector fields on isolated complete intersection singularities

Details Remarks on contact structures and vector fields on isolated complete intersection singularities Remarks on contact structures and vector fields on isolated complete intersection singularities

2006-09-15

arxiv.org/abs/math/0609448v1

Mathematics

Algebraic Geometry

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Remarks on contact structures and vector fields on isolated complete intersection singularities does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Remarks on contact structures and vector fields on isolated complete intersection singularities, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Remarks on contact structures and vector fields on isolated complete intersection singularities will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-411211