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arXiv · 2408.03799

An abundance-type result for the tangent bundles of smooth Fano varieties

Juanyong Wang
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Abstract

In this paper we prove the following abundance-type result: for any smooth Fano variety $X$, the tangent bundle $T_X$ is nef if and only if it is big and semiample in the sense that the tautological line bundle $\mathscr{O}_{\mathbb{P}T_X}(1)$ is so, by which we establish a weak form of the Campana-Peternell conjecture (Camapan-Peternell, 1991).

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Juanyong Wang. 2024-08-07. An abundance-type result for the tangent bundles of smooth Fano varieties. https://arxiv.org/abs/2408.03799

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