Compactified spaces of holomorphic curves in complex Grassmann manifolds

In this paper we study the topology of a compactification of the space of holomorphic maps of fixed degree from ℂP¹ into a finite-dimensional complex Grassmann manifold. We show that there is a homotopy equivalence through a range, increasing with the degree, between these compact spaces and an infinite-dimensional complex Grassmann manifold. These compact spaces form a direct system indexed by the degree, and the direct limit is homotopy equivalent to an infinite-dimensional complex Grassmann manifold.