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# Examples of Fano manifolds with non-pseudoeffective tangent bundle

Abstract : 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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https://hal.univ-cotedazur.fr/hal-02998483
Contributor : Andreas Höring <>
Submitted on : Tuesday, November 10, 2020 - 3:16:11 PM
Last modification on : Thursday, November 12, 2020 - 12:11:43 PM

### Identifiers

• HAL Id : hal-02998483, version 1
• ARXIV : 2003.09476

### Citation

Andreas Höring, Jie Liu, Feng Shao. Examples of Fano manifolds with non-pseudoeffective tangent bundle. 2020. ⟨hal-02998483⟩

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