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XVII.—The Tacnodal Form of Humbert's Sextic*
Published online by Cambridge University Press: 14 February 2012
Synopsis
Humbert's 5-nodal plane sextic first appeared in his 1894 paper. Its canonical curve C was identified in 1951, when it was shown that the sextic is the outcome of projecting C from one of its own chords on to a plane.
In this present paper it is remarked that there are 60 chords of C such that the projection has two tacnodes, each a confluence of two of Humbert's 5 nodes, and an equation is found for this tacnodal curve.
A certain specialization permits C to be invariant for a group of 32, not merely 16, projectivities. Further specializations, described in the proper place, permit groups of orders 64, 96, 160. The resulting tacnodal sextics have groups of birational self-transformations isomorphic to these.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 68 , Issue 3 , 1970 , pp. 257 - 269
- Copyright
- Copyright © Royal Society of Edinburgh 1970
References
References to Literature
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