TOPOLOGY OF REAL SCHLAFLI SIX-LINE CONFIGURATIONS ON CUBIC SURFACES AND IN RP3

摘要

A famous configuration of 27 lines on a non-singular cubic surface in P-3 contains remarkable subconfigurations, and in particular the ones formed by six pairwise disjoint lines. We study such six-line configurations in the case of real cubic surfaces from a topological viewpoint, as configurations of six disjoint lines in the real projective 3-space, and show that the condition that they lie on a cubic surface implies a very special property of homogeneity. This property distinguishes them in the list of 11 deformation types of configurations formed by six disjoint lines in RP3.