On rank 2 vector bundles on Fano manifolds

Details On rank 2 vector bundles on Fano manifolds On rank 2 vector bundles on Fano manifolds

2011-04-08

arxiv.org/abs/1104.1490v3

Mathematics

Algebraic Geometry

Updated version with applications to Hartshorne's conjecture

Scientific paper

In this work we deal with vector bundles of rank two on a Fano manifold $X$ with $b_2=b_4=1$. We study the nef and pseudoeffective cones of the corresponding projectivizations and how these cones are related to the decomposability of the vector bundle. As consequences, we obtain the complete list of $\P^1$-bundles over $X$ that have a second $\P^1$-bundle structure, classify all the uniform rank two vector bundles on this class of Fano manifolds and show the stability of indecomposable Fano bundles (with one exception on $\P^2$).

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