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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

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