Journal of Mathematics of Kyoto University

Fundamental groups of spaces of holomorphic maps and group actions

Kohhei Yamaguchi

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Abstract

For integers $d \geq 0$ and $1 \neq k \neq n$, let $\mathrm{Hol}_{d}(\mathbb{C}P^{k},\mathbb{C}P^{n})$ denote the space consisting of all holomorphic maps $f : \mathbb{C}P^{k}\to \mathbb{C}P^{n}$ of degree $d$. We shall compute the fundamental group of $\mathrm{Hol}_{d}(\mathbb{C}P^{k},\mathbb{C}P^{n})$ and study $\mathrm{PGL}_{n+1}(\mathbb{C})$-action on it.

Article information

Source
J. Math. Kyoto Univ., Volume 44, Number 3 (2004), 479-492.

Dates
First available in Project Euclid: 14 August 2009

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1250283079

Digital Object Identifier
doi:10.1215/kjm/1250283079

Mathematical Reviews number (MathSciNet)
MR2103778

Zentralblatt MATH identifier
1088.55010

Subjects
Primary: 55P10: Homotopy equivalences
Secondary: 55P15: Classification of homotopy type 55P35: Loop spaces 58D15: Manifolds of mappings [See also 46T10, 54C35]

Citation

Yamaguchi, Kohhei. Fundamental groups of spaces of holomorphic maps and group actions. J. Math. Kyoto Univ. 44 (2004), no. 3, 479--492. doi:10.1215/kjm/1250283079. https://projecteuclid.org/euclid.kjm/1250283079


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