1948•Mathematical Proceedings of the Cambridge Philosophical SocietyRequires access

Combinants of a pencil of quadric surfaces (III)

John A. Todd

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Abstract

The two previous papers of this series dealt with the determination of the complete system of combinantal covariants and contravariants of a pencil of quadric surfaces. The present paper is concerned with combinantal forms involving line-complexes, and with certain syzygies which exist between these forms. It is essentially a preparation for the determination of the complete system of combinantal line-complexes of the pencil, which will be carried out explicitly in the next paper of the series.

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The two previous papers of this series dealt with the determination of the complete system of combinantal covariants and contravariants of a pencil of quadric surfaces. The present paper is concerned with combinantal forms involving line-complexes, and with certain syzygies which exist between these forms. It is essentially a preparation for the determination of the complete system of combinantal line-complexes of the pencil, which will be carried out explicitly in the next paper of the series.

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Available abstract

The two previous papers of this series dealt with the determination of the complete system of combinantal covariants and contravariants of a pencil of quadric surfaces. The present paper is concerned with combinantal forms involving line-complexes, and with certain syzygies which exist between these forms. It is essentially a preparation for the determination of the complete system of combinantal line-complexes of the pencil, which will be carried out explicitly in the next paper of the series.

Key concepts: Pencil (optics), Quadric, Series (stratigraphy), Mathematics, Line (geometry), Algebra over a field, Pure mathematics, Geometry

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