Abundance of Real Lines on Real Projective Hypersurfaces

Date

2013-01-01

Author

Finashin, Sergey
Kharlamov, Viatcheslav

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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.

URI

https://hdl.handle.net/11511/47179

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Department of Mathematics, Article