On the polar degree of projective hypersurfaces

Details On the polar degree of projective hypersurfaces On the polar degree of projective hypersurfaces

2011-08-12

arxiv.org/abs/1108.2676v2

Mathematics

Algebraic Geometry

11 pages, 2 figures. Fixed minor typos. Final version, to appear in J. London Math. Soc

Scientific paper

Given a hypersurface in the complex projective $n$-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.

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