Generalization flocks of \(\mathcal Q^+(3,q)\) (Q2761646)
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scientific article; zbMATH DE number 1686125
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Generalization flocks of \(\mathcal Q^+(3,q)\) |
scientific article; zbMATH DE number 1686125 |
Statements
7 January 2002
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flock
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spread
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nearfield
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Segre variety
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Veronese variety
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Singer cycle
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0.91218096
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0.8667714
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0.8642824
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0.8615717
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0.8570243
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0.85667455
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Generalization flocks of \(\mathcal Q^+(3,q)\) (English)
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A flock of the hyperbolic quadric \(Q^+(3,1)\) is a partition of the quadric into \(q+1\) irreducible conics; flocks are equivalent to certain classes of translation planes of rank 2 over their kernel. NEWLINENEWLINENEWLINEMotivated by the fact that \(Q^+(3,1)\) is the smallest Segre variety \(S_{1,1}\), the authors extend the notion of a flock to the Segre variety \(S_{n,n}\); flocks of \(S_{n,n}\) are defined as partitions of \(S_{n,n}\) into Veronese varieties. Again, there are close connections to translation planes; for instance, ``linear'' flocks yield nearfield planes.
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