Abundance of Real Lines on Real Projective Hypersurfaces

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2013-01-01

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Finashin, Sergey

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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

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Department of Mathematics, Article

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Citation Formats

S. Finashin, “Abundance of Real Lines on Real Projective Hypersurfaces,” INTERNATIONAL MATHEMATICS RESEARCH NOTICES, pp. 3639–3646, 2013, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/47179.