Abundance of Real Lines on Real Projective Hypersurfaces


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FİNASHİN S. , Kharlamov V.

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, no.16, pp.3639-3646, 2013 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2013
  • Doi Number: 10.1093/imrn/rns135
  • Title of Journal : INTERNATIONAL MATHEMATICS RESEARCH NOTICES
  • Page Numbers: pp.3639-3646

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.