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On the stability of the tangent bundle of Fano manifolds

Andreas Steffens
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Abstract

By using the classification of Fano 3-folds we prove: Let $X$ be Fano 3-fold. Assume that the tangent bundle $T_X$ of $X$ is not stable (i.e. semi-stable or unstable). Then $b_2\geq 2$ and a relative tangent sheaf $T_{X/Y}$ of a contraction $f:X\longrightarrow Y$ of an extremal face on $X$ is a destabilising subsheaf of $T_X$.

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BibTeXRIS

Andreas Steffens. 1994-07-10. On the stability of the tangent bundle of Fano manifolds. https://arxiv.org/abs/alg-geom/9407004

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