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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
##### Keywords:
rank-2 Fano bundles
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