论文标题
嵌入式紧凑型复杂流形和更高的编构叶的邻居的等效性
Equivalence of Neighborhoods of Embedded Compact Complex Manifolds and Higher Codimension Foliations
论文作者
论文摘要
我们考虑$ n+d $尺寸复杂歧管中的嵌入式$ n $二维紧凑型复杂歧管。作为Grauert正式原则计划的一部分，我们对社区的全体形态分类感兴趣。我们将提供条件，以确保$ M_ {n+d} $的$ C_N $的社区对其正常捆绑包的零部分的附近是Biholomorphic。这扩展了Arnold在表面中复杂圆环的邻域的结果。我们还证明了$ m_ {n+d} $以$ c_n $作为紧凑型叶子的$ m_ {n+d} $存在，将UEDA的理论扩展到了高的编质案例。这两个问题似乎都是一个线性化问题，涉及由解决方案引起的小除数条件。
We consider an embedded $n$-dimensional compact complex manifold in $n+d$ dimensional complex manifolds. We are interested in the holomorphic classification of neighborhoods as part of Grauert's formal principle program. We will give conditions ensuring that a neighborhood of $C_n$ in $M_{n+d}$ is biholomorphic to a neighborhood of the zero section of its normal bundle. This extends Arnold's result about neighborhoods of a complex torus in a surface. We also prove the existence of a holomorphic foliation in $M_{n+d }$ having $C_n$ as a compact leaf, extending Ueda's theory to the high codimension case. Both problems appear as a kind linearization problem involving small divisors condition arising from solutions to their cohomological equations.
