Asymptotically Holomorphic Families of Symplectic Submanifolds
Asymptotically Holomorphic Families of Symplectic Submanifolds
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辛子流形的渐近全纯族
DOI：
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
D. Auroux
中科院分区：
文献类型：
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作者：
D. Auroux
抽象的。我们在紧辛流形中构造了广泛的辛子流形，作为向量丛渐近全纯截面的零集，该零集是通过用复线丛的大幂张量任意向量丛获得的，该复线丛的第一个陈类是辛形式。我们还表明，渐近地，从给定向量束构造的子流形的所有序列都是同位素的。此外，我们证明了类似于构造子流形的 Lefschetz 超平面定理的结果。
Abstract. We construct a wide range of symplectic submanifolds in a compact symplectic manifold as the zero sets of asymptotically holomorphic sections of vector bundles obtained by tensoring an arbitrary vector bundle by large powers of the complex line bundle whose first Chern class is the symplectic form. We also show that, asymptotically, all sequences of submanifolds constructed from a given vector bundle are isotopic. Furthermore, we prove a result analogous to the Lefschetz hyperplane theorem for the constructed submanifolds.