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Spaces of holomorphic maps between complex projective spaces of degree one. (English) Zbl 1165.55302
Summary: For an integer \(d\geq 0\), let \(\text{Hol}_d(\mathbb CP^k,\mathbb CP^n)\) denote the space consisting of all holomorphic maps \(f:\mathbb CP^k\to\mathbb CP^n\) of degree \(d\). We study the homogeneous space structure of \(\text{Hol}_d(\mathbb CP^k,\mathbb CP^n)\) for the case \(d=1\). In particular we explicitly determine its homotopy type.

MSC:
55P10 Homotopy equivalences in algebraic topology
55P35 Loop spaces
55P15 Classification of homotopy type
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