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Irregular threefolds which possess anticanonical systems

Published online by Cambridge University Press:  24 October 2008

L. Roth
L. Roth
Affiliation:
Imperial CollegeLondon
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Extract

The present paper is a sequel to a previous study (7) of the completely regular threefolds which possess anticanonical systems, i.e. for which the virtual canonical system, reversed in sign, is effective of positive order. On any such threefold the process of successive adjunction, applied to any linear system of surfaces, must terminate; we have thus to deal with a special case of the adjunction problem for the regular threefolds. By making certain simplifying hypotheses (such as irreducibility and absence of base elements) concerning the anticanonical systems, one can classify the threefolds in broad outline and show that, provided the anticanonical systems are sufficiently ample, the corresponding threefolds are either unirational or birational.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 52 , Issue 4 , October 1956 , pp. 617 - 622
Copyright
Copyright © Cambridge Philosophical Society 1956

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References

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