Rational homotopy stability for the spaces of rational maps
Abstract
Let x0 n (1, X) be the space of based holomorphic maps of degree n from 1 into a simply connected algebraic variety X. Under some condition we prove that the map x0 n (1, X). x0d n (1, X). obtained by compositing f ∈ x0 n (1, X) with g(z)=zd, z ∈ 1 induces rational homotopy equivalence up to some dimension, which tends to infinity as the degree grows.
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