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Specialization of Cremona transformations

Published online by Cambridge University Press:  26 February 2010

J. G. Semple  and
J. A. Tyrrell
J. G. Semple
Affiliation:
King's College London.
J. A. Tyrrell
Affiliation:
King's College London.
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Extract

Let V = V2n be the Segre product variety of two n–dimensional complex projective spaces. Then any Cremona transformation of Sn into (regarded as an irreducible algebraic system of ∞n ordered pairs of points) is represented on V by an irreducible n-dimensional subvariety H which satisfies (on V) the algebraic equivalence

where Si, j is a subvariety of V and m1, …, mn–1 are positive integers. We call m1, …, mn–1 the characters of T noting that, numerically,

Type
Research Article
Information
Mathematika , Volume 15 , Issue 2 , December 1968 , pp. 171 - 177
Copyright
Copyright © University College London 1968

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References

1.Hudson, H. P., Cremona transformations in plane and space (Cambridge, 1927).Google Scholar
2.Hudson, H. P., “On the 3, 3 birational transformation in three dimensions (Second Paper)”, Proc. London Math. Soc., (2), 10 (1912), 15–47.CrossRefGoogle Scholar
3.Room, T. G., Geometry of Determinantal Manifolds (Cambridge, 1938).Google Scholar
4.Semple, J. G., “Cremona transformations of space of four dimensions by means of quadrics and the reverse transformations”, Phil. Trans. Royal Soc., A, 228 (1929), 331–376.Google Scholar
5.Semple, J. G., “On quadratic representations of the lines of four-dimensional space”, Proc. London Math. Soc., (2), 30 (1929), 500–512.Google Scholar