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- W409019183 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." @default.
- W409019183 created "2016-06-24" @default.
- W409019183 creator A5033412614 @default.
- W409019183 date "2015-05-26" @default.
- W409019183 modified "2023-09-27" @default.
- W409019183 title "When are the Cayley-Salmon lines conjugate?" @default.
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