## 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 language | English (US) |
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Pages (from-to) | 299-312 |

Number of pages | 14 |

Journal | Topology and its Applications |

Volume | 126 |

Issue number | 1-2 |

DOIs | |

State | Published - Nov 30 2002 |

## All Science Journal Classification (ASJC) codes

- Geometry and Topology