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Fano bundles over \(P^ 3\) and \(Q_ 3\). (English) Zbl 0705.14016
Let E be a vector bundle of rank \(r\geq 2\) on a smooth complex projective variety M. E is called a Fano bundle if its projectivization P(E) is a Fano manifold. In this paper, the authors prove that Fano bundles exist only on Fano manifolds. Furthermore, they determine all rank-2 Fano bundles on \({\mathbb{P}}^ 3\) with \(c_ 1=0, -1\) and they discuss rank-2 Fano bundles over a 3-dimensional smooth quadric Q with \(c_ 1=0\), \(c_ 2=2\) and with \(c_ 1=-1\), \(c_ 2=1\).
Reviewer: R.M.Miró-Roig

MSC:
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14J45 Fano varieties
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