论文标题
$ \ bar {\ partial} $ - laplacian与Nef Line Bundle相关的特征值估算值
An eigenvalue estimate for the $\bar{\partial}$-Laplacian associated to a nef line bundle
论文作者
论文摘要
我们研究$ \ bar {\ partial} $ - laplacian在$ l^{k} $中的表格上，在紧凑的复合歧管上的nef线束的高功率，并估算其相应的特征值小于或等于$λ$的相应特征值的数量。特别是，$λ= 0 $ case给出了相应同胞组的顺序的渐近估计。它有助于概括grauert-riemenschneider的猜想。最后，我们在伪有效的线条捆绑包上讨论$λ= 0 $ case。
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 $λ$. In particular, the $λ=0$ 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 $λ=0$ case on a pseudo-effective line bundle.
