Abundance of Real Lines on Real Projective Hypersurfaces
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, sa.16, ss.3639-3646, 2013 (SCI-Expanded, Scopus)
- 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
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- 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.