Marion Boucrot

In 1849, G.Salmon proved that any nonsingular cubic surface in the projective space of dimension 3 of an algebraically closed field contains exactly 27 lines. 

A. Cayley had already shown that there are only finitely many lines on such surfaces. In this talk, I will present an elementary proof of this result, written by S.Lazarus. I will also explain why the three hypothesis are necessary, using counter examples, and present the work of L. Schläfli on the case of real cubic surfaces.