Topology of Real Schlafli Six-Line Configurations on Cubic Surfaces and\n in mathbbRP³

2017/08/05 by Sergey Finashin, Finashin, Sergey, Remzi̇ye Arzu Zabun +1
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Mathematics and Applications #Computational Geometry and Mesh Generation

paper · pdf · doi:10.48550/arxiv.1708.01814

Abstract

A famous configuration of 27 lines on a non-singular cubic surface in\n mathbb P³ contains remarkable subconfigurations, and in particular the ones\nformed by six pairwise disjoint lines. We study such six-line configurations in\nthe case of real cubic surfaces from topological viewpoint, as configurations\nof six disjoint lines in the real projective 3-space, and show that the\ncondition that they lie on a cubic surface implies a very special property of\n it homogeneity. This property distinguish them in the list of 11 deformation\ntypes of configurations formed by six disjoint lines in mathbbRP³.\n

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