Abundance of Real Lines on Real Projective Hypersurfaces

作者:Finashin Sergey; Kharlamov Viatcheslav*
来源:International Mathematics Research Notices, 2013, (16): 3639-3646.
DOI:10.1093/imrn/rns135

摘要

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.

  • 出版日期2013