论文标题

多项式图的模量空间及其全态指数:I。在具有多个固定点的情况下,通用特性

The Moduli Space of Polynomial Maps and Their Holomorphic Indices: I. Generic Properties in the Case of Having Multiple Fixed Points

论文作者

Sugiyama, Toshi

论文摘要

遵循作者以前的作品,我们继续考虑计算一个复杂变量的多项式的仿射共轭类的数量,当时给出了其无序的全态固定点指数的收集。在作者以前的论文中,多项式没有多个固定点,就已经完全解决了问题。在本文中,我们考虑具有多个固定点的情况,并获取每个给定程度和每个给定数量的固定点的全体形态固定点索引的通用公式。

Following the author's previous works, we continue to consider the problem of counting the number of affine conjugacy classes of polynomials of one complex variable when its unordered collection of holomorphic fixed point indices is given. The problem was already solved completely in the case that the polynomials have no multiple fixed points, in the author's previous papers. In this paper, we consider the case of having multiple fixed points, and obtain the formulae for generic unordered collections of holomorphic fixed point indices, for each given degree and for each given number of fixed points.

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