Abundance of Real Lines on Real Projective Hypersurfaces

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FİNASHİN S., Kharlamov V.

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, sa.16, ss.3639-3646, 2013 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2013
  • Doi Numarası: 10.1093/imrn/rns135
  • Dergi Adı: INTERNATIONAL MATHEMATICS RESEARCH NOTICES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.3639-3646
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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.