模空间中的带前缀的曲线

IF 1.7 1区 数学 Q1 MATHEMATICS
Xavier Buff, A. Epstein, Sarah C. Koch
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引用次数: 6

摘要

文摘:我们研究了某些代数曲线在三次多项式的模空间和二次有理映射的模空间中的几何。给定$k\geq0$,(在二次有理映射的情况下为$k\neq1$),我们证明了具有前周期$k$的前缀临界点的映射的共轭类集合是不可约的代数曲线(在$\Bbb{C}$上)。然后,我们研究了一个密切相关的问题,即阶$D\geq2$的单临界多项式的共轭类集与周期前临界点的不可约性(在$\Bbb{Q}$上)。我们的证明纯粹是算术的;它们依赖于一个结果,该结果提供了$\Bbb{C}$上的不可约性等价于$\Bbb{Q}$上不可约的充分条件,并依赖于不可约度的广义艾森斯坦准则。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Prefixed curves in moduli space
abstract:We study the geometry of certain algebraic curves in the moduli space of cubic polynomials, and in the moduli space of quadratic rational maps. Given $k\geq 0$, ($k\neq 1$ in the case of quadratic rational maps), we show that the set of conjugacy classes of maps with a prefixed critical point of preperiod $k$, is an algebraic curve that is irreducible (over $\Bbb{C}$). We then study a closely related question concerning the irreducibility (over $\Bbb{Q}$) of the set of conjugacy classes of unicritical polynomials, of degree $D\geq 2$, with a preperiodic critical point. Our proofs are purely arithmetic; they rely on a result providing sufficient conditions under which irreducibility over $\Bbb{C}$ is equivalent to irreducibility over $\Bbb{Q}$, and on a generalized Eisenstein criterion for irreducibility.
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来源期刊
CiteScore
3.20
自引率
0.00%
发文量
35
审稿时长
24 months
期刊介绍: The oldest mathematics journal in the Western Hemisphere in continuous publication, the American Journal of Mathematics ranks as one of the most respected and celebrated journals in its field. Published since 1878, the Journal has earned its reputation by presenting pioneering mathematical papers. It does not specialize, but instead publishes articles of broad appeal covering the major areas of contemporary mathematics. The American Journal of Mathematics is used as a basic reference work in academic libraries, both in the United States and abroad.
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