On the degree of Polar Transformations -- An approach through Logarithmic Foliations
Algebraic Geometry
2010-04-02 v1
Abstract
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 is determined by the zero locus of . 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.
Cite
@article{arxiv.0705.1867,
title = {On the degree of Polar Transformations -- An approach through Logarithmic Foliations},
author = {Thiago Fassarella and Jorge Vitório Pereira},
journal= {arXiv preprint arXiv:0705.1867},
year = {2010}
}