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

1993/01/24 by Martin A. Guest, Guest, Martin A. · 1 citation
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Advanced Combinatorial Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.alg-geom/9301005

Abstract

Let X be a compact toric variety. Let Hol denote the space of based holomorphic maps from CP¹ 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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• Homological stability and weak approximation

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