Title

On Projective Manifolds with Two P-bundle Structures

Document Type

Article

Publication Date

1988

Abstract

We investigate whether a projective manifold V which is a P 1-bundle over a projective manifold X with the same homology type of P r can have another P-bundle structure over some projective manifold Y; moreover, in the affirmative case we find restrictions on the topology of Y. Among the corollaries we prove that if V is a P l-bundle over P 4 and over a 4-fold Y not of general type, then either V = P 4 x P 4, V = P(T P 4), or, possibly, Y is a rational Fano 4-fold many properties of which are known. Further generalizations naturally arising from the geometry of flag manifolds are discussed.

Comments

This article was originally published in Annals of Global Analysis and Geometry, volume 6, issue 1, in 1988. DOI: 10.1007/BF00054608

Peer Reviewed

1

Copyright

Kluwer Academic Publishers