Abundance of real lines on real projective hypersurfaces

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.

5 pages; http://imrn.oxfordjournals.org/cgi/content/abstract/rns135?

References in corpus (3)

• Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions
• Opening Mirror Symmetry on the Quintic
• Welschinger invariants of real del Pezzo surfaces of degree $\ge 2$

Cited by in corpus (10)

• An Arithmetic Count of the Lines on a Smooth Cubic Surface
• Abundance of 3-planes on real projective hypersurfaces
• Real Lines on Random Cubic Surfaces
• Segre indices and Welschinger weights as options for invariant count of real lines
• A wall crossing formula for degrees of real central projections
• Halving spaces and lower bounds in real enumerative geometry
• Lower bounds in real algebraic geometry and orientability of real toric varieties
• On wall-crossing invariance of certain sums of Welschinger numbers
• Qualitative aspects of counting real rational curves on real K3 surfaces
• Random fields and the enumerative geometry of lines on real and complex hypersurfaces