The structure of rational and ruled symplectic 4-manifolds
The structure of rational and ruled symplectic 4-manifolds
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DOI：
10.1090/s0894-0347-1990-1049697-8
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发表时间：
1990-09
影响因子：
3.9
通讯作者：
D. Mcduff
中科院分区：
文献类型：
--
作者：
D. Mcduff
研究了紧辛4流形（V, w）的结构，其中包含S2的一个非负自交数的辛嵌入副本C。这样的一对（V， C, w）被称为极小，如果，另外，开放流形V C不包含异常曲线（即，辛嵌入的自交-1的2球）。我们证明了每一个这样的对（V， C, w）覆盖了一个极小对(V， C， C()，这个极小对（V， C， C()）可以通过吹动V C中有限个不相交的例外曲线而从V中得到。进一步，所考虑的流形对族（V， C, w）在吹动和吹动下是封闭的。接下来我们给出一个可能的最小对的完整列表。我们证明了V是辛形态的？p2的标准形式，或紧曲面上唯一由其上同调类决定的辛结构的s2束。此外，可以选择这种复形态，使得C可以变成CP2中的复线或二次线，或者，当V是束时，变成束的一根纤维或一段。纽约州立大学石溪分校数学系，纽约州石溪分校11794-3651电子邮件地址：dusa@math.sunysb.edu本内容于2016年4月27日星期三05:10:07 UTC从207.46.13.145下载
This paper investigates the structure of compact symplectic 4-manifolds (V, w) which contain a symplectically embedded copy C of S2 with nonnegative self-intersection number. Such a pair (V, C, w) is called minimal if, in addition, the open manifold V C contains no exceptional curves (i.e., symplectically embedded 2-spheres with self-intersection -1) . We show that every such pair (V, C, w) covers a minimal pair (V, C, c() which may be obtained from V by blowing down a finite number of disjoint exceptional curves in V C. Further, the family of manifold pairs (V, C, w) under consideration is closed under blowing up and down. We next give a complete list of the possible minimal pairs. We show that V is symplectomorphic either to ? p2 with its standard form, or to an S2-bundle over a compact surface with a symplectic structure which is uniquely determined by its cohomology class. Moreover, this symplectomorphism may be chosen so that it takes C either to 2 a complex line or quadric in CP2, or, in the case when V is a bundle, to a fiber or section of the bundle. DEPARTMENT OF MATHEMATICS, STATE UNIVERSITY OF NEW YORK AT STONY BROOK, STONY BROOK, NEW YORK 11794-3651 E-mail address: dusa@math.sunysb.edu This content downloaded from 207.46.13.145 on Wed, 27 Apr 2016 05:10:07 UTC All use subject to http://about.jstor.org/terms