Abundance of Real Lines on Real Projective Hypersurfaces

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FİNASHİN S., Kharlamov V.

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, no.16, pp.3639-3646, 2013 (SCI-Expanded) identifier identifier


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.