First homology of a real cubic is generated by lines

Sergey Finashin, Viatcheslav Kharlamov

Published 2019-11-16Version 1

We suggest a short proof of O.Benoist and O.Wittenberg theorem (arXiv:1907.10859) which states that for each real non-singular cubic hypersurface $X$ of dimension $\ge 2$ the real lines on $X$ generate the whole group $H_1(X(\Bbb R);\Bbb Z/2)$.