The space of rational maps on P¹

الأصل · EN

The set of morphisms:¹→¹ of degree d is parametrized by an affine open subset of ²ᵈ⁺¹. We consider the action of ₂ on induced by the conjugation action of ₂ on rational maps; that is, f∈₂ acts on via ᶠ=f⁻¹∘∘ f. The quotient space =/₂ arises very naturally in the study of discrete dynamical systems on ¹. We prove that exists as an affine integral scheme over, that ₂ is isomorphic to Ų, and that the natural completion of ₂ obtained using geometric invariant theory is isomorphic to ². These results, which generalize results of Milnor over, should be useful for studying the arithmetic properties of dynamical systems.