The 27 lines on a cubic surface
星期四, 2 二月, 2023 - 17:00
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.
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