Several injectivity theorems on compact Kähler manifolds

Abstract

In this short note, we use the Bochner technique and the Hodge theory in complex differential geometry to prove several injectivity results for the cohomology of holomorphic vector bundles on compact Kähler manifolds, which generalize Enoki’s original injectivity theorem.

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Acknowledgements

The author would like to thank the referee for carefully reading the paper and for valuable suggestions.

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Correspondence to Chunle Huang.

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Huang, C. Several injectivity theorems on compact Kähler manifolds. Geom Dedicata 208, 89–95 (2020). https://doi.org/10.1007/s10711-020-00511-z

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Keywords

  • Injectivity theorem
  • Compact Kähler manifolds
  • Bochner technique
  • Hodge theory

Mathematics Subject Classification (2000)

  • 32L10
  • 32Q15