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


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FİNASHİN S. , Zabun R. A.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, vol.147, no.9, pp.3665-3674, 2019 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 147 Issue: 9
  • Publication Date: 2019
  • Doi Number: 10.1090/proc/14340
  • Title of Journal : PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
  • Page Numbers: pp.3665-3674

Abstract

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.