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On the structure of 4-folds with a hyperplane section which is a P1 bundle over a surface that fibres over a curve

Published online by Cambridge University Press:  22 January 2016

Maria Lucia Fania ,
Eiichi Sato  and
Andrew John Sommese
Maria Lucia Fania
Affiliation:
Istituto di Matematica Università dell’ Aquila, Via Roma 33 67100 L’Aquila, Italia
Eiichi Sato
Affiliation:
Department of Mathematics College of General Education Kyushu University, Kyushu, 810, Japan
Andrew John Sommese
Affiliation:
Department of Mathematics University of Notre Dame, Notre Dame, Indiana 46556, U. S. A.
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In this article we want to analyze the structure of a 4 dimensional projective variety X which has a smooth ample divisor A that is a P1 bundle π : A→S over a smooth surface S.

In [Fa+So], as a consequence of a more general result, the first and third authors determined the structure of X in the case the base S of the P1 bundle A has a cover with h2,0()≠0. Here we look at the remaining cases except for those surfaces which are the projectivization of a stable rank two vector bundle over a curve (the result is obviously true for S rational).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 108 , December 1987 , pp. 1 - 14
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1987

References

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