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arXiv · 1201.2897

Abundance of real lines on real projective hypersurfaces

S. Finashin·V. Kharlamov
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Abstract

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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S. Finashin, V. Kharlamov. 2012-01-13. Abundance of real lines on real projective hypersurfaces. https://doi.org/10.1093/imrn%2Frns135

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