On the degree of Polar Transformations -- An approach through Logarithmic Foliations

Details On the degree of Polar Transformations -- An approach through Logarithmic Foliations On the degree of Polar Transformations -- An approach through Logarithmic Foliations

2007-05-14

arxiv.org/abs/0705.1867v1

Selecta Mathematica, Volume 13, Number 2 / October, 2007

Mathematics

Algebraic Geometry

Scientific paper

10.1007/s00029-007-0040-x

We investigate the degree of the polar transformations associated to a certain class of multi-valued homogeneous functions. In particular we prove that the degree of the pre-image of generic linear spaces by a polar transformation associated to a homogeneous polynomial $F$ is determined by the zero locus of $F$. For zero dimensional-dimensional linear spaces this was conjecture by Dolgachev and proved by Dimca-Papadima using topological arguments. Our methods are algebro-geometric and rely on the study of the Gauss map of naturally associated logarithmic foliations.

Affiliated with

Also associated with

No associations

Rating

On the degree of Polar Transformations -- An approach through Logarithmic Foliations 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 On the degree of Polar Transformations -- An approach through Logarithmic Foliations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the degree of Polar Transformations -- An approach through Logarithmic Foliations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-365351