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

David E. Hurtubise, Marc D. Sanders

Research output: Contribution to journalArticlepeer-review

Abstract

We construct a compactification of the space of holomorphic curves of fixed degree in a finite-dimensional complex Grassmann manifold using basic algebra. The algebraic compactification is defined as the quotient of n-tuples of linearly independent elements in a ℂ[z]-module. The complex analytic structure on the space of holomorphic curves of fixed degree extends to the algebraic compactification. We show that there is a homotopy equivalence through a range increasing with the degree between the compactified spaces and an infinite-dimensional complex Grassmann manifold. These compact spaces form a direct system, indexed by the degree, whose direct limit is homotopy equivalent to an infinite-dimensional complex Grassmann manifold.

Original languageEnglish (US)
Pages (from-to)299-312
Number of pages14
JournalTopology and its Applications
Volume126
Issue number1-2
DOIs
StatePublished - Nov 30 2002

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

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