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Examples of Fano manifolds with non-pseudoeffective tangent bundle

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arxiv 2003.09476 v1 pith:BB72CA2D submitted 2020-03-20 math.AG

Examples of Fano manifolds with non-pseudoeffective tangent bundle

classification math.AG
keywords bundlefanopezzotangentanticanonicalauthorsbeencharacterisation
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Let $X$ be a Fano manifold. While the properties of the anticanonical divisor $-K_X$ and its multiples have been studied by many authors, the positivity of the tangent bundle $T_X$ is much more elusive. We give a complete characterisation of the pseudoeffectivity of $T_X$ for del Pezzo surfaces, hypersurfaces in the projective space and del Pezzo threefolds.

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