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Nets of conics

Published online by Cambridge University Press:  24 October 2008

C. T. C. Wall
C. T. C. Wall
Affiliation:
University of Liverpool
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Extract

Segre's classification of pencils of quadrics is well known, and appears in standard texts such as (1), (2). By contrast, other linear systems of quadrics do not lend them-selves to a similar exhaustive treatment. Here we discuss the simplest case, that of nets of conics. The result is intrinsically interesting, and involves some pleasant geometry. As well as deriving a list of types, and enumerating their properties, we study the elementary geometrical properties of the partition of the space Ω of nets into equivalence classes (or strata). We work over the field ℝ of real numbers, after performing preliminary calculations over ℂ.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 81 , Issue 3 , May 1977 , pp. 351 - 364
Copyright
Copyright © Cambridge Philosophical Society 1977

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References

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