On the polar degree of projective hypersurfaces
Algebraic Geometry
2014-02-26 v2
Abstract
Given a hypersurface in the complex projective -space we prove several known formulas for the degree of its polar map by purely algebro-geometric methods. Furthermore, we give formulas for the degree of its polar map in terms of the degrees of the polar maps of its components. As an application, we classify the plane curves with polar map of low degree, including a very simple proof of I. Dolgachev's classification of homaloidal plane curves.
Keywords
Cite
@article{arxiv.1108.2676,
title = {On the polar degree of projective hypersurfaces},
author = {Thiago Fassarella and Nivaldo Medeiros},
journal= {arXiv preprint arXiv:1108.2676},
year = {2014}
}
Comments
11 pages, 2 figures. Fixed minor typos. Final version, to appear in J. London Math. Soc