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arXiv · 1204.4793

A classification theorem on Fano bundles

Roberto Muñoz·Gianluca Occhetta·Luis E. Solá Conde
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Abstract

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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Roberto Muñoz, Gianluca Occhetta, Luis E. Solá Conde. 2012-04-21. A classification theorem on Fano bundles. https://arxiv.org/abs/1204.4793

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