论文标题
第3级和4度射态性的自多态基因座的基因座。
Automorphism loci for degree 3 and degree 4 endomorphisms of the projective line
论文作者
论文摘要
令$ f $为投射线的内态性。通过投影线性群体的要素，在这种形态的空间上有一种自然的共轭作用。众所周知，给定$ f $的一组自动形态或稳定器组是有限的组。我们确定明确的家庭，这些家庭将所有内态性参数化，以$ \ bar {\ mathbb {q}} $ $ 3 $和度量$ 4 $具有非平凡的自动形态，\ textit {automorphism locus locus}的模态空间的模型空间。我们在动态系统的适当模量空间中分析了这些基因座的几何形状。此外，对于每个地图家族，我们研究了$ \ mathbb {q} $的可能结构 - 在专业化下发生的有理前碘点。
Let $f$ be an endomorphism of the projective line. There is a natural conjugation action on the space of such morphisms by elements of the projective linear group. The group of automorphisms, or stabilizer group, of a given $f$ for this action is known to be a finite group. We determine explicit families that parameterize all endomorphisms defined over $\bar{\mathbb{Q}}$ of degree $3$ and degree $4$ that have a nontrivial automorphism, the \textit{automorphism locus} of the moduli space of dynamical systems. We analyze the geometry of these loci in the appropriate moduli space of dynamical systems. Further, for each family of maps, we study the possible structures of $\mathbb{Q}$-rational preperiodic points which occur under specialization.
