### 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 |

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### All Science Journal Classification (ASJC) codes

- Geometry and Topology

### Cite this

*Topology and its Applications*,

*126*(1-2), 299-312. https://doi.org/10.1016/S0166-8641(02)00090-1

}

*Topology and its Applications*, vol. 126, no. 1-2, pp. 299-312. https://doi.org/10.1016/S0166-8641(02)00090-1

**An algebraic compactification for spaces of holomorphic curves in complex Grassmann manifolds.** / Hurtubise, David Edward; Sanders, Marc D.

Research output: Contribution to journal › Article

TY - JOUR

T1 - An algebraic compactification for spaces of holomorphic curves in complex Grassmann manifolds

AU - Hurtubise, David Edward

AU - Sanders, Marc D.

PY - 2002/11/30

Y1 - 2002/11/30

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0038013882&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0038013882&partnerID=8YFLogxK

U2 - 10.1016/S0166-8641(02)00090-1

DO - 10.1016/S0166-8641(02)00090-1

M3 - Article

AN - SCOPUS:0038013882

VL - 126

SP - 299

EP - 312

JO - Topology and its Applications

JF - Topology and its Applications

SN - 0166-8641

IS - 1-2

ER -