Abundance of real lines on real projective hypersurfaces
Algebraic Geometry
2012-06-26 v1 Geometric Topology
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.
Keywords
Cite
@article{arxiv.1201.2897,
title = {Abundance of real lines on real projective hypersurfaces},
author = {S. Finashin and V. Kharlamov},
journal= {arXiv preprint arXiv:1201.2897},
year = {2012}
}
Comments
5 pages; http://imrn.oxfordjournals.org/cgi/content/abstract/rns135?