The varieties of tangent lines to hypersurfaces in projective spaces

2010/12/10 by Atsushi Ikeda, Ikeda, Atsushi
Mathematics · #14C05 #14M15 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14C05 #msc:14M15

paper · pdf · doi:10.48550/arxiv.1012.2186

10 pages

arxiv created 2010/12/10 · arxiv updated 2010/12/13

Abstract

For a hypersurface in a projective space, we consider the set of pairs of a point and a line in the projective space such that the line intersects the hypersurface at the point with a fixed multiplicity. We prove that this set of pairs forms a smooth variety for a general hypersurface.

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