Szurek, Michał; Wiśniewski, Jarosław A. Fano bundles over \(P^ 3\) and \(Q_ 3\). (English) Zbl 0705.14016 Pac. J. Math. 141, No. 1, 197-208 (1990). 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 Cited in 2 ReviewsCited in 24 Documents MSC: 14F05 Sheaves, derived categories of sheaves, etc. (MSC2010) 14J45 Fano varieties Keywords:rank-2 Fano bundles PDFBibTeX XMLCite \textit{M. Szurek} and \textit{J. A. Wiśniewski}, Pac. J. Math. 141, No. 1, 197--208 (1990; Zbl 0705.14016) Full Text: DOI