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The conjugacy locus of Cayley-Salmon lines.
- Source :
-
Advances in Geometry . Jan2018, Vol. 18 Issue 1, p41-54. 14p. - Publication Year :
- 2018
-
Abstract
- Given six points on a conic, Pascal's theorem gives rise to a configuration called the hexagrammum mysticum. It contains 20 Steiner points and 20 Cayley-Salmon lines. By a classical theorem due to von Staudt, the Steiner points fall into 10 conjugate pairs with reference to the conic; but this is not true of the C-S lines for a general choice of six points. We show that the C-S lines are pairwise conjugate precisely when the original sextuple is tri-symmetric. The variety of tri-symmetric sextuples turns out to be arithmetically Cohen-Macaulay of codimension two. We determine its SL2-equivariant minimal resolution. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 1615715X
- Volume :
- 18
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Advances in Geometry
- Publication Type :
- Academic Journal
- Accession number :
- 127683895
- Full Text :
- https://doi.org/10.1515/advgeom-2017-0045