Asymptotics of spectral function of lower energy forms and Bergman kernel of semi-positive and big line bundles
Asymptotics of spectral function of lower energy forms and Bergman kernel of semi-positive and big line bundles
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DOI：
10.4310/cag.2014.v22.n1.a1
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发表时间：
2011-12
影响因子：
0.7
通讯作者：
Chin-Yu Hsiao;G. Marinescu
中科院分区：
文献类型：
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作者：
Chin-Yu Hsiao;G. Marinescu
在本文中，我们研究了全纯线束高张量幂上对应于小平拉普拉斯谱下部的谱函数的渐近行为。这意味着该函数在线束曲率非简并的集合上完全渐近展开。作为应用，我们在曲率为正的集合上获得完整 Khler 流形上的伴随半正线丛的 Bergman 核渐近。我们还证明了具有严格正曲率电流的奇异埃尔米特度量的大线丛的渐近性。在这种情况下，完全渐近在度量的奇异轨迹之外成立。
In this paper we study the asymptotic behaviour of the spectral function corre- sponding to the lower part of the spectrum of the Kodaira Laplacian on high tensor powers of a holomorphic line bundle. This implies a full asymptotic expansion of this function on the set where the curvature of the line bundle is non-degenerate. As application we obtain the Bergman kernel asymptotics for adjoint semi-positive line bundles over complete Khler manifolds, on the set where the curvature is positive. We also prove the asymptotics for big line bundles endowed with singular Hermitian metrics with strictly positive curvature current. In this case the full asymptotics holds outside the singular locus of the metric.