The topology of the space of rational curves on a toric variety

Details The topology of the space of rational curves on a toric variety The topology of the space of rational curves on a toric variety

1993-01-24

arxiv.org/abs/alg-geom/9301005v2

Mathematics

Algebraic Geometry

25 pages, AMS-TeX 2.1 (substantially revised and updated)

Scientific paper

Let $X$ be a compact toric variety. Let $Hol$ denote the space of based holomorphic maps from $CP^1$ to $X$ which lie in a fixed homotopy class. Let $Map$ denote the corresponding space of continuous maps. We show that $Hol$ has the same homotopy groups as $Map$ up to some (computable) dimension. The proof uses a description of $Hol$ as a space of configurations of labelled points, where the labels lie in a partial monoid determined by the fan of $X$.

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