Abundance of 3-planes on real projective hypersurfaces

Sergey Finashin, Viatcheslav Kharlamov

We show that a generic real projective $n$-dimensional hypersurface of odd degree $d$, such that $4(n-2)=\left(\genfrac{}{}{0ex}{}{d+3}{3}\right)$, contains "many" real 3-planes, namely, in the logarithmic sc…