Abundance of Real Lines on Real Projective Hypersurfaces

Abstract

We show that a generic real projective n-dimensional hypersurface of degree\n2n-1 contains "many" real lines, namely, not less than (2n-1)!!, which is\napproximately the square root of the number of complex lines. This estimate is\nbased on the interpretation of a suitable signed count of the lines as the\nEuler number of an appropriate bundle.\n