An eigenvalue estimate for the ∂-Laplacian associated to a nef line bundle

2020/03/11 by Wu, Jingcao
#32J25 #32L05 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2003.05187

Abstract

We study the ∂-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.

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