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

David Edward Hurtubise, Marc D. Sanders

Research output: Contribution to journalArticle

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

Fingerprint

Holomorphic Curve
Grassmann Manifold
Complex Manifolds
Compactification
Basic Algebra
Direct Limit
Homotopy Equivalence
Space Form
Compact Space
Homotopy
Quotient
Linearly
Module
Range of data

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

Cite this

@article{c6b201fa162843d5839825e880ad5806,
title = "An algebraic compactification for spaces of holomorphic curves in complex Grassmann manifolds",
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.",
author = "Hurtubise, {David Edward} and Sanders, {Marc D.}",
year = "2002",
month = "11",
day = "30",
doi = "10.1016/S0166-8641(02)00090-1",
language = "English (US)",
volume = "126",
pages = "299--312",
journal = "Topology and its Applications",
issn = "0166-8641",
publisher = "Elsevier",
number = "1-2",

}

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

In: Topology and its Applications, Vol. 126, No. 1-2, 30.11.2002, p. 299-312.

Research output: Contribution to journalArticle

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 -