Moduli spaces for families of rational maps on P
نویسنده
چکیده
Let φ : P → P be a rational map defined over a field K. We construct the moduli space Md(N) parameterizing conjugacy classes of degree-d maps with a point of formal period N and present an algebraic proof that M2(N) is geometrically irreducible for N > 1. Restricting ourselves to maps φ of arbitrary degree d ≥ 2 such that h ◦ φ ◦ h = φ for some nontrivial h ∈ PGL2 `
منابع مشابه
Topology and arithmetic of resultants, I
We consider the interplay of point counts, singular cohomology, étale cohomology, eigenvalues of the Frobenius and the Grothendieck ring of varieties for two families of varieties: spaces of rational maps and moduli spaces of marked, degree d rational curves in P. We deduce as special cases algebro-geometric and arithmetic refinements of topological computations of Segal, Cohen–Cohen–Mann–Milgr...
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