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Pseudo-Abelian varieties

Published online by Cambridge University Press:  24 October 2008

L. Roth
L. Roth
Affiliation:
Imperial College of Science London, S.W. 7
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Extract

It is a familiar fact that the Picard surface (or hyperelliptic surface of rank 1) admits a completely transitive permutable continuous group of ∞2 automorphisms. There are, however, other non-scrollar surfaces which possess continuous groups of automorphisms, namely, the elhptic surfaces. Every elliptic surface V2 contains a pencil of birationally equivalent elhptic curves, which are the trajectories of the group in question; it also contains a second, elliptic, pencil of birationally equivalent curves; the intersection number of the two pencils is an important character, known as the determinant of V2. Just as any Picard surface can be mapped on a multiple Picard surface of divisor unity, so V2 can be mapped on a multiple elliptic surface of determinant unity, the branch curve (if any) corresponding to a certain number of trajectories.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 50 , Issue 3 , July 1954 , pp. 360 - 371
Copyright
Copyright © Cambridge Philosophical Society 1954

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