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The algebra of symmetric tensors on smooth projective varieties

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Abstract

In this paper, we discuss the ℂ-algebra H0(X, S•TX) for a smooth complex projective variety X. We compute it in some simple examples, and give a sharp bound on its Krull dimension. Then we propose a conjectural characterization of non-uniruled projective manifolds with pseudo-effective tangent bundle.

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Acknowledgements

The first author is indebted to Feng Shao for several useful comments and references. The second author thanks S. Druel for useful communication. The second author was supported by the National Key Research and Development Program of China (Grant No. 2021YFA1002300), National Natural Science Foundation of China (Grant No. 12288201) and the CAS Project for Young Scientists in Basic Research (Grant No. YSBR-033).

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Authors and Affiliations

  1. CNRS, Laboratoire J.-A. Dieudonné, Université Côte d’Azur, F-06108, Nice, France

    Arnaud Beauville

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

    Jie Liu

Authors
  1. Arnaud Beauville
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  2. Jie Liu
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Correspondence to Arnaud Beauville.

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In Memory of Professor Gang Xiao

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Beauville, A., Liu, J. The algebra of symmetric tensors on smooth projective varieties. Sci. China Math. (2024). https://doi.org/10.1007/s11425-023-2284-4

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  • DOI: https://doi.org/10.1007/s11425-023-2284-4

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