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Chow forms of congruences

Published online by Cambridge University Press:  01 January 1997

LUIS GIRALDO  and
IGNACIO SOLS
LUIS GIRALDO
Affiliation:
Departamento de Álgebra, Fac. Matemáticas, Universidad Complutense de Madrid 28040 Madrid, Spain
IGNACIO SOLS
Affiliation:
Departamento de Álgebra, Fac. Matemáticas, Universidad Complutense de Madrid 28040 Madrid, Spain
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Abstract

Let V be a 4-dimensional complex space. A congruence Y is an integral surface of the Grassmann variety G = Gr(2, 4) of 2-dimensional subspaces V2 of V (we denote by Vi a subspace of V of dimension i). They have been extensively studied by both classical and modern geometers. We bring to their study the tool of Chow forms, characterizing them by differential equations, following the program of M. Green and I. Morrison [3]. The first results in this direction are due to Cayley ([1], [2]) and are rederived in [3]. Our results share much of the geometrical flavour of Cayley's.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 121 , Issue 1 , January 1997 , pp. 31 - 37
Copyright
© Cambridge Philosophical Society 1997

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