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Abundance of Real Lines on Real Projective Hypersurfaces
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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
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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.
Subject Keywords
Enumerative geometry
URI
https://hdl.handle.net/11511/47179
Journal
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
DOI
https://doi.org/10.1093/imrn/rns135
Collections
Department of Mathematics, Article