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On generic nefness of tangent sheaves

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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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Acknowledgements

The author would like to express his gratitude to Stéphane Druel and Burt Totaro for reading the preliminary version of this paper and warm encouragement. He is grateful to Junyan Cao for pointing out Theorem 1.8 to him. He would like to thank Jun Li, Chen Jiang, Claire Voisin, Yuan Wang and Jian Xiao for general discussions. He would like to thank the referees for reading the paper carefully and providing helpful remarks. The author is supported by the National Key R &D Program of China (No. 2021YFA1002300).

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  1. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Wenhao Ou

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Ou, W. On generic nefness of tangent sheaves. Math. Z. 304, 58 (2023). https://doi.org/10.1007/s00209-023-03306-6

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