An algebraic compactification for spaces of holomorphic curves in complex Grassmann manifolds
type: Item
instance of: scholarly article
title: An algebraic compactification for spaces of holomorphic curves in complex Grassmann manifolds
zbMATH Open document ID: 1029.32010
DOI: 10.1016/S0166-8641(02)00090-1
published in: Topology and its Applications
publication date: 2003-04-02T00:00:00Z
review text: 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.
reviewed by: Vagn Lundsgaard Hansen
Mathematics Subject Classification ID: 32Q99
Mathematics Subject Classification ID: 32C18
Mathematics Subject Classification ID: 55P10
Mathematics Subject Classification ID: 53D35
zbMATH DE Number: 1891213
zbMATH Keywords: algebraic compactification
zbMATH Keywords: space of holomorphic curves
zbMATH Keywords: homotopy equivalence
author: David E. Hurtubise
author: M. Sanders
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1891213