P^1上有理映射族的模空间
Moduli spaces for families of rational maps on P^1
摘要：
设φ：P^1 --> P^1是定义在域K上的有理映射。构造了以形式周期N为点的d次映射共轭类的参数化模空间M_d（N），并给出了M_2（N）对N>1几何不可约的代数证明.限制我们自己到任意次数d >= 2的映射φ，使得对于PGL_2中的某个非平凡h，合成h^{-1} φ h = φ，我们证明了用形式周期N的点参数化这些映射的模空间对无穷多个N是几何可约的。
英文摘要：
Let phi: P^1 --> P^1 be a rational map defined over a field K. We construct the moduli space M_d(N) parameterizing conjugacy classes of degree-d maps with a point of formal period N and present an algebraic proof that M_2(N) is geometrically irreducible for N>1. Restricting ourselves to maps phi of arbitrary degree d >= 2 such that the composition h^{-1} phi h = phi for some nontrivial h in PGL_2, we show that the moduli space parameterizing these maps with a point of formal period N is geometrically reducible for infinitely many N.
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