An algebraic compactification for spaces of holomorphic curves in complex Grassmann manifolds (Q1867187)

The authors construct an algebraic compactification of the space Hol\(_d({\mathbb C}P^1, G_{n.n+k}({\mathbb C}))\) of holomorphic curves of degree \(d\) in a complex Grassman manifold by taking a quotient of \(n\)-tuples of linearly independen elements in a suitable \({\mathbb C}[z]\)-module. They prove that the complex analytic structure on the space of holomorphic curves extends to the algebraic compactification. Furthermore, it is proved that there is a homotopy equivalence through a range increasing with the degree \(d\) between the compactified spaces and an infinite-dimensional Grassmann manifold. In the introduction, the problem is carefully put into context.