论文标题
伯格曼内核的渐近学（主论文）
Asymptotic of Bergman Kernel (Master Thesis)
论文作者
论文摘要
在这篇主论文中，我们在伯格曼内核的渐近膨胀方面给出了一个新的证明，该伯格曼内核是在线束的曲率为正且满足局部光谱间隙条件的点上的位置。要点是引入合适的半古典符号空间和相关的符号符号演算，该符号是受Hsiao和Savale最近工作启发的。特别是，我们在某些半阳性线束的积极部分上建立了渐近膨胀的存在。
In this master thesis, we give a new proof on the pointwise asymptotic expansion for Bergman kernel of a hermitian holomorphic line bundle on the points where the curvature of the line bundle is positive and satisfy local spectral gap condition. The main point is to introduce a suitable semi-classical symbol space and related symbolic calculus inspired from recent work of Hsiao and Savale. Particularly, we establish the existence of pointwise asymptotic expansion on the positive part for certain semi-positive line bundles.
