Abundance of real lines on real projective hypersurfaces

Details Abundance of real lines on real projective hypersurfaces Abundance of real lines on real projective hypersurfaces

2012-01-13

arxiv.org/abs/1201.2897v1

Mathematics

Algebraic Geometry

5 pages

Scientific paper

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.

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