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Some loci in S5 associated with systems of conics in a plane
Published online by Cambridge University Press: 14 November 2011
Synopsis
If the conic α, a0x2 + a1y2 + a2z2 + 2a3yz + 2a4zx + 2a5xy=0, is represented by the point (a0, a1, a2, a3, a4, a5) of S5, the transforms of α by projectivities that fix a second conic ω will generally be represented by points of a threefold in S5 containing (a0, a1,…, a5). It is shown that this threefold is in general a rational sextic belonging to an ∞2 family, that is composed of ∞1 sets of projectively equivalent threefolds. Special, exceptional members of the family are discussed.
Equations for the threefold are found in terms of the mutual projection invariants of ω and α.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 84 , Issue 1-2 , 1979 , pp. 93 - 107
- Copyright
- Copyright © Royal Society of Edinburgh 1979
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