On the Zeroes of Meromorphic Vector-Fields
On the Zeroes of Meromorphic Vector-Fields
复制标题
关于亚纯矢量场的零点
DOI：
10.1007/978-3-642-49197-9_4
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发表时间：
1970
期刊：
影响因子：
--
通讯作者：
R. Bott
中科院分区：
文献类型：
--
作者：
P. Baum;R. Bott
LetMbe a compact complex analytic manifold and letxbe a holomorphic vector-field onM. In an earlier paper by one of us (see [2]) it was shown that the behavior ofxnear its zeroes determined all the Chern numbers ofMand the nature of this determination was explicitly given wherexhad only nondegenerate zeroes. The primary purpose of this note is to extend this result to meromorphic fields, or equivalently to sections s ofT⊗LwhereTis the holomorphic tangent bundle toMandLis a holomorphic line bundle. We will also drop the non-degeneracy assumption of the zeroes of s, but we treat only the case where s vanishes at isolated points {p}.
