On generic nefness of tangent sheaves

Wenhao Ou

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arXiv · 1703.03175

On generic nefness of tangent sheaves

Wenhao Ou

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Abstract

We show that the tangent bundle of a projective manifold with nef anticanonical class is generically nef. That is, its restriction to a curve cut out by general sufficiently ample divisors is a nef vector bundle. This confirms a conjecture of Peternell. As a consequence, the second Chern class of such a manifold has non-negative intersections with ample divisors. We also investigate under which conditions these positivities are strict, and answer a question of Yau.

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Wenhao Ou. 2017-03-09. On generic nefness of tangent sheaves. https://arxiv.org/abs/1703.03175

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