Spaces of morphisms from a projective space to a toric variety

TL;DR

This paper extends stability results for spaces of rational maps from projective spaces to toric varieties, showing that similar stability properties hold for continuous morphisms and improving bounds for curves.

Contribution

It generalizes the stability theorem from rational maps to continuous morphisms into toric varieties and refines bounds for the stabilization dimension in the case of curves.

Findings

Stability theorem extends to continuous morphisms from CP^m to X

Improved bounds for stabilization dimension for curves

Results hold for smooth compact toric varieties

Abstract

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.