Topology of Real Schlafli Six-Line Configurations on Cubic Surfaces and in $\mathbb{RP}^3$

摘要

A famous configuration of 27 lines on a non-singular cubic surface in$\mathbb P^3$ contains remarkable subconfigurations, and in particular the onesformed by six pairwise disjoint lines. We study such six-line configurations inthe case of real cubic surfaces from topological viewpoint, as configurationsof six disjoint lines in the real projective 3-space, and show that thecondition that they lie on a cubic surface implies a very special property of{\it homogeneity}. This property distinguish them in the list of 11 deformationtypes of configurations formed by six disjoint lines in $\mathbb{RP}^3$.