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Abundance of Real Lines on Real Projective Hypersurfaces

Finashin, Sergey
Kharlamov, Viatcheslav
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.