Affordable Access

When are the Cayley-Salmon lines conjugate?

Authors
  • Chipalkatti, Jaydeep
Type
Preprint
Publication Date
May 26, 2015
Submission Date
May 26, 2015
Identifiers
arXiv ID: 1505.07144
Source
arXiv
License
Yellow
External links

Abstract

Given six points on a conic, Pascal's theorem gives rise to a well-known configuration called the \emph{hexagrammum mysticum}. It consists of, amongst other things, twenty Steiner points and twenty Cayley-Salmon lines. It is a classical theorem due to von Staudt that the Steiner points fall into ten conjugate pairs with reference to the conic; but this is not true of the C-S lines for a general choice of six points. It is shown in this paper that the C-S lines are pairwise conjugate precisely when the original sextuple is~\emph{tri-involutive}. The variety of tri-involutive sextuples turns out to be arithmetically Cohen-Macaulay of codimension two. We determine its $SL_2$-equivariant minimal resolution.

Report this publication

Statistics

Seen <100 times