# The Topology of the Space of Holomorphic Maps with Bounded Multiplicity

### Kohhei Yamaguchi

University of Electro-Communications, Tokyo, Japan

## 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