• Corpus ID: 212657416

An eigenvalue estimate for the $\bar{\partial}$-Laplacian associated to a nef line bundle

@article{Wu2020AnEE,
  title={An eigenvalue estimate for the \$\bar\{\partial\}\$-Laplacian associated to a nef line bundle},
  author={Jingcao Wu},
  journal={arXiv: Complex Variables},
  year={2020}
}
  • Jingcao Wu
  • Published 11 March 2020
  • Mathematics
  • arXiv: Complex Variables
We study the $\bar{\partial}$-Laplacian on forms taking values in $L^{k}$, a high power of a nef line bundle on a compact complex manifold, and give an estimate of the number of the eigenforms whose corresponding eigenvalues smaller than or equal to $\lambda$. In particular, the $\lambda=0$ case gives an asymptotic estimate for the order of the corresponding cohomology groups. It helps to generalize the Grauert--Riemenschneider conjecture. At last, we discuss the $\lambda=0$ case on a pseudo… 
1 Citation

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