Invariants and projections of six lines in projective space (Q2719042)
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scientific article; zbMATH DE number 1597932
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Invariants and projections of six lines in projective space |
scientific article; zbMATH DE number 1597932 |
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Invariants and projections of six lines in projective space (English)
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14 May 2001
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line configurations
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double-six
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six-tuple of lines in \(\mathbb{P}^3\)
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JFM 02.0570.02
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JFM 13.0490.01
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0.90296173
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0.8876412
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0.8832246
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The author investigates the relations between the invariants describing a configuration of an ordered six-tuple of lines in \({\mathbb P}^3\) and the invariants describing the configuration of the ordered six-tuple of lines in \({\mathbb P}^2\) arising by a projection of the former from a point in \({\mathbb P}^3\), especially under the additional assumption that the six lines in the plane are tangent to a conic. The method is quite algebraic, explicit equations are given for the varieties in question. Connections to classical results from \textit{J. Todd} [Proc. Camb. Philos. Soc. 29, 52-68 (1933; Zbl 0006.12601)], \textit{V. Hierholzer} [Math. Ann. 2, 563-587 (1870; JFM 02.0570.02)], and \textit{F. Schur} [Math. Ann. 18, 1-33 (1881; JFM 13.0490.01)] are pointed out.
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