Residual indices of holomorphic maps relative to singular curves of fixed points on surfaces
Residual indices of holomorphic maps relative to singular curves of fixed points on surfaces
复制标题
全纯映射相对于曲面上不动点奇异曲线的残差指数
DOI：
10.1007/s002090100352
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发表时间：
2002
影响因子：
0.8
通讯作者：
F. Tovena
中科院分区：
文献类型：
--
作者：
Filippo Bracci;F. Tovena
设M是一个二维复流形，设M是一个全纯映射，它逐点固定一条（可能）奇异、紧致、约化且整体不可约的曲线。我们给出了一个在C点处退化的概念。证明了f在一点非退化当且仅当它在C的每一点都非退化。当f在C上非退化时，我们定义了f在C上每一点的残差指数。证明了C的指数之和等于C的自相交数。
LetMbe a two-dimensional complex manifold and letbe a holomorphic map that fixes pointwise a (possibly) singular, compact, reduced and globally irreducible curve. We give a notion ofdegeneracyoffat a point ofC. It turns out thatfis non-degenerate at one point if and only if it is non-degenerate at every point ofC. Whenfis non-degenerate onC, we define a residual index forfat each point ofC. Then we prove that the sum of the indices is equal to the self-intersection number ofC.