For a complex (quasi-) projective variety X ⊆ ℂP_N_ with π2(X) = ℤ and an integer d ≥ 0, let Hol_d_∗(_S_2, X) denote the space consisting of all basepoint preserving d holomorphic maps f from _S_2 to X with degree d. We study the topology of certain subspaces of Hol_d_∗ (_S_2, X) deﬁned using the concept of multiplicity of roots, and we d show that the Atiyah–Jones–Segal type theorem (, ) holds for these subspaces if X is belong to a certain family of complex quasi-projective varieties.
Cite this article
Kohhei Yamaguchi, The Topology of the Space of Holomorphic Maps with Bounded Multiplicity. Publ. Res. Inst. Math. Sci. 42 (2006), no. 1, pp. 83–100DOI 10.2977/PRIMS/1166642059