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On projective manifolds with twoP-bundle structures

✍ Scribed by Antonio Lanteri; Daniele C. Struppa

Publisher
Springer
Year
1988
Tongue
English
Weight
266 KB
Volume
6
Category
Article
ISSN
0232-704X

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✦ Synopsis

We investigate whether a projective manifold V which is a P'-bundle over a projective manifold X with the same homology type of P' 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-bundle over P 4 and over a 4-fold Y not of general type, then either V = P 4 X P 4 , V = P(T4), 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.

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