论文标题
伯格曼捆绑以及对紧凑复合歧管的几何形状的应用
Bergman bundles and applications to the geometry of compact complex manifolds
论文作者
论文摘要
我们介绍了在Hermitian歧管X上附加的Bergman束的概念，假设歧管X是紧凑的 - 尽管结果在很大程度上是局部的。伯格曼捆绑包是某种无限的尺寸，非常丰富的希尔伯特捆绑包，其纤维与复杂单位球上的标准L $ {}^2 $ hardy空间同构；但是，该捆绑包仅在实际分析类别中是局部微不足道的，其复杂结构是强烈扭曲的。我们计算伯格曼束的Chern曲率，并表明它是严格的积极的。作为一种潜在的应用，我们研究了在plurigenera的不变性中，在紧凑型k {ä} hler歧管的一般情况下，SIU的长期且仍未解决。
We introduce the concept of Bergman bundle attached to a hermitian manifold X, assuming the manifold X to be compact - although the results are local for a large part. The Bergman bundle is some sort of infinite dimensional very ample Hilbert bundle whose fibers are isomorphic to the standard L${}^2$ Hardy space on the complex unit ball; however the bundle is locally trivial only in the real analytic category, and its complex structure is strongly twisted. We compute the Chern curvature of the Bergman bundle, and show that it is strictly positive. As a potential application, we investigate a long standing and still unsolved conjecture of Siu on the invariance of plurigenera in the general situation of polarized families of compact K{ä}hler manifolds.
