A classification theorem on Fano bundles

Details A classification theorem on Fano bundles A classification theorem on Fano bundles

2012-04-21

arxiv.org/abs/1204.4793v1

Mathematics

Algebraic Geometry

Scientific paper

In this paper we classify rank two Fano bundles $\cE$ on Fano manifolds satisfying $H^2(X,\Z)\cong H^4(X,\Z)\cong\Z$. The classification is obtained via the computation of the nef and pseudoeffective cones of the projectivization ${\mathbb{P}}(\cE)$, that allows us to obtain the cohomological invariants of $X$ and $\cE$. As a by-product we discuss Fano bundles associated to congruences of lines, showing that their varieties of minimal rational tangents may have several linear components.

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