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arXiv · 0705.1867

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

Thiago Fassarella·Jorge Vitório Pereira
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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 $F$ 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.

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Thiago Fassarella, Jorge Vitório Pereira. 2007-05-14. On the degree of Polar Transformations -- An approach through Logarithmic Foliations. https://doi.org/10.1007/s00029-007-0040-x

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