论文标题
将Nirenberg-Spencer关于全体形态嵌入的问题扩展到全体形态嵌入家庭
Extending Nirenberg-Spencer's question on holomorphic embeddings to families of holomorphic embeddings
论文作者
论文摘要
Nirenberg和Spencer提出了一个问题，即在正常束足够正时，在复杂歧管中紧凑的复合物submanifold的细菌是否取决于其无限顺序的无限邻域。为了研究包括自由理性曲线在内的较大类次曼群的问题，我们在Submanifolds及其无穷小社区的家庭中重新制定了一个问题。当Submanifolds没有非零矢量字段时，我们证明只有一阶街区就可以对重新制定的问题有肯定的答案是足够的。当子策略确实具有非零矢量字段时，我们会在Submanifolds具有某些不错的变形属性的附加假设下获得对该问题的肯定答案，该属性适用于自由理性曲线。作为一个应用程序，我们获得了Picard Number 1的Fano歧管的Cartan-Fubini类型扩展定理的更强版本。我们还提出了潜在的应用程序对投射K3表面的超平面段的应用。
Nirenberg and Spencer posed the question whether the germ of a compact complex submanifold in a complex manifold is determined by its infinitesimal neighborhood of finite order when the normal bundle is sufficiently positive. To study the problem for a larger class of submanifolds, including free rational curves, we reformulate the question in the setting of families of submanifolds and their infinitesimal neighborhoods. When the submanifolds have no nonzero vector fields, we prove that it is sufficient to consider only first-order neighborhoods to have an affirmative answer to the reformulated question. When the submanifolds do have nonzero vector fields, we obtain an affirmative answer to the question under the additional assumption that submanifolds have certain nice deformation properties, which is applicable to free rational curves. As an application, we obtain a stronger version of the Cartan-Fubini type extension theorem for Fano manifolds of Picard number 1. We also propose a potential application on hyperplane sections of projective K3 surfaces.
