论文标题
kahler型球的嵌入到符号歧管中
Kahler-type embeddings of balls into symplectic manifolds
论文作者
论文摘要
考虑将域不相交联合到符号歧管$ m $中的符合性嵌入。这种嵌入称为kahler-type，或分别称为驯服，如果相对于某些（不是先验固定的，kahler-type）的复杂结构是与符号形式兼容的$ M $，或者分别被其驯服的。假设$ m $以下任务：复杂的投影空间（具有标准的符号形式），均匀的圆环或配备非理性Kahler型符号形式的K3表面。然后，任何两种脱节球融合到$ m $的kahler型嵌入都可以通过在同源性上琐碎作用的符号呈现。如果嵌入相对于与象征性形式兼容的复杂结构，并位于$ M $上的Kahler型复杂结构的相同连接组件中，则可以选择符号呈符号，因此可以将符号呈现为平稳地对身份。对于某些$ m $和某些脱节球，我们精确地描述了对球嵌入球的障碍物，使球嵌入到$ m $ $ m $中。尤其是，符合量是$ l^n $均等球（对于任何$ l $）存在的唯一障碍，将$ l^n $相等的球嵌入到$ n $ dimensional-diperional-Diperional-Diperional-Dipersional的复合物中，并具有标准的符号形式，并且具有任何可能的不同的球或K3表面，并配备了不合理形式，并具有任何可能的不同的球。我们还表明，符号体积是唯一的障碍物，即存在相等的球，多齿轮或平行牵引的脱节工会的驯服嵌入到配备通用的kahler型符号形式的圆环中。对于K3表面，对于球和平行教的也是如此。
Consider a symplectic embedding of a disjoint union of domains into a symplectic manifold $M$. Such an embedding is called Kahler-type, or respectively tame, if it is holomorphic with respect to some (not a priori fixed, Kahler-type) complex structure on $M$ compatible with the symplectic form, or respectively tamed by it. Assume that $M$ either of the following: a complex projective space (with the standard symplectic form), an even-dimensional torus or a K3 surface equipped with an irrational Kahler-type symplectic form. Then any two Kahler-type embeddings of a disjoint union of balls into $M$ can be mapped into each other by a symplectomorphism acting trivially on the homology. If the embeddings are holomorphic with respect to complex structures compatible with the symplectic form and lying in the same connected component of the space of Kahler-type complex structures on $M$, then the symplectomorphism can be chosen to be smoothly isotopic to the identity. For certain $M$ and certain disjoint unions of balls we describe precisely the obstructions to the existence of Kahler-type embeddings of the balls into $M$. In particular, symplectic volume is the only obstruction for the existence of Kahler-type embeddings of $l^n$ equal balls (for any $l$) into the $n$-dimensional complex projective space with the standard symplectic form and of any number of possibly different balls into a torus or a K3 surface, equipped with an irrational symplectic form. We also show that symplectic volume is the only obstruction for the existence of tame embeddings of disjoint unions of equal balls, polydisks, or parallelepipeds, into a torus equipped with a generic Kahler-type symplectic form. For balls and parallelepipeds the same is true for K3 surfaces.
