Contractibility of the space of rational maps
نویسندگان
چکیده
منابع مشابه
The Space of Rational Maps on P1
The set of morphisms : P 1 ! P 1 of degree d is parametrized by an aane open subset Rat d of P 2d+1. We consider the action of SL 2 on Rat d induced by the conjugation action of SL 2 on rational maps; that is, f 2 SL 2 acts on via f = f ?1 f. The quotient space M d = Rat d =SL 2 arises very naturally in the study of discrete dynamical systems on P 1. We prove that M d exists as an aane integral...
متن کاملThe Moduli Space of Quadratic Rational Maps
Let M2 be the space of quadratic rational maps f : P 1 → P , modulo the action by conjugation of the group of Möbius transformations. In this paper a compactification X of M2 is defined, as a modification of Milnor’s M 2 ' CP , by choosing representatives of a conjugacy class [f ] ∈ M2 such that the measure of maximal entropy of f has conformal barycenter at the origin in R, and taking the clos...
متن کاملThe Space of Rational Maps on P
The set of morphisms φ : P → P of degree d is parametrized by an affine open subset Ratd of P . We consider the action of SL2 on Ratd induced by the conjugation action of SL2 on rational maps; that is, f ∈ SL2 acts on φ via φ = f ◦ φ ◦ f . The quotient space Md = Ratd/SL2 arises very naturally in the study of discrete dynamical systems on P. We prove that Md exists as an affine integral scheme ...
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ژورنال
عنوان ژورنال: Inventiones mathematicae
سال: 2012
ISSN: 0020-9910,1432-1297
DOI: 10.1007/s00222-012-0392-5