First homology of a real cubic is generated by lines

Abstract

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 $H_1(X(\mathbb{R});\mathbb{Z}/2)$.

arXiv comment7 pages