In this paper we study the space of morphisms from a complex projective space to a compact smooth toric variety X. It is shown that the first author's stability theorem for the spaces of rational maps from CP m to CP n extends to the spaces of continuous morphisms from CP m to X essentially, with the same proof. In the case of curves, our result improves the known bounds for the stabilization dimension.2010 Mathematics Subject Classification. Primary: 58D15; Secondary: 32Q55.
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