Zeroes of holomorphic vector fields and Grothendieck duality theory
Zeroes of holomorphic vector fields and Grothendieck duality theory
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全纯向量场的零点和格罗滕迪克对偶理论
DOI：
10.1090/s0002-9947-1977-0445562-5
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发表时间：
1977
期刊：
影响因子：
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通讯作者：
N. O'brian
中科院分区：
文献类型：
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作者：
N. O'brian
利用Grothendieck的对偶理论讨论了Atiyah和Bott的全纯不动点公式。该方法适用于具有任意孤立不动点的紧致复解析流形的自同态。然后，对于自同态属于由具有孤立零点的全纯向量场生成的加群的情形，给出了不动点指数的表达式。文中给出了一个应用实例。证明了这些结果的两个推广。第一个是关于加群在基流形上的作用具有足够齐性的全纯向量丛，第二个是关于代数簇上的加群作用的全纯向量丛。
The holomorphic fixed point formula of Atiyah and Bott is discussed in terms of Grothendieck's theory of duality. The treatment is valid for an endomorphism of a compact complex-analytic manifold with arbitrary isolated fixed points. An expression for the fixed point indices is then derived for the case where the endomorphism belongs to the additive group generated by a holomorphic vector field with isolated zeroes. An application and some examples are given. Two generalisations of these results are also proved. The first deals with holomorphic vector bundles having sufficient homogeneity properties with respect to the action of the additive group on the base manifold, and the second with additive group actions on algebraic varieties.