Abundance of Real Lines on Real Projective Hypersurfaces
Copyright policy )Abundance of Real Lines on Real Projective Hypersurfaces
We show that a generic real projective n-dimensional hypersurface of degree 2n-1 contains "many" real lines, namely, not less than (2n-1)!!, which is approximately the square root of the number of complex lines. This estimate is based on the interpretation of a suitable signed count of the lines as the Euler number of an appropriate bundle.
5 pages; http://imrn.oxfordjournals.org/cgi/content/abstract/rns135?
Mathematics - Algebraic Geometry, Mathematics - Geometric Topology, 14N15, 14P25, 14J80, [MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG], FOS: Mathematics, Geometric Topology (math.GT), Algebraic Geometry (math.AG), [MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]
Mathematics - Algebraic Geometry, Mathematics - Geometric Topology, 14N15, 14P25, 14J80, [MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG], FOS: Mathematics, Geometric Topology (math.GT), Algebraic Geometry (math.AG), [MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]
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