Rational homotopy stability for the spaces of rational maps

2002/11/07 by Jiayuan Lin, Lin, Jiayuan
Mathematics · #14E05 #14F45 #55P62 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG #math.AT #msc:14E05 #msc:14F45 #msc:55P62

paper · pdf · doi:10.48550/arxiv.math/0211137

arxiv created 2002/11/07 · openalex publication_date 2002/11/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \Hol_x0^{\bf n} (\C¶¹, X) be the space of based holomorphic maps of degree \bf n from \C¶¹ into a simply connected algebraic variety X. Under some condition we prove that the map \map \Hol_x0^{\bf n} (\C¶¹, X). \Hol_x0^d\bf n (\C¶¹, X). obtained by compositing f ∈ \Hol_x0^{\bf n} (\C¶¹, X) with g(z)=z^d, z ∈ \C¶¹ induces rational homotopy equivalence up to some dimension, which tends to infinity as the degree grows.

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