JournalsprimsVol. 42, No. 1pp. 83–100

The Topology of the Space of Holomorphic Maps with Bounded Multiplicity

  • Kohhei Yamaguchi

    University of Electro-Communications, Tokyo, Japan
The Topology of the Space of Holomorphic Maps with Bounded Multiplicity cover
Download PDF

Abstract

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 ([1], [11]) 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. 83–100

DOI 10.2977/PRIMS/1166642059