http://dx.doi.org/10.15446/recolma.v48n1.45194

¹CINVESTAV-IPN, México, D.F., México. Email: jacob@math.cinvestav.mx
²Institut de Mathématiques de Jussieu, Paris, France. Email: erendira.munguia@gmail.com

In this note 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 CPⁿ 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.

Key words: Toric variety, Stone-Weierstrass Theorem, Spaces of toric morphisms, simplicial resolution.

En esta nota se estudia el espacio de morfismos de un espacio proyectivo complejo a una variedad tórica compacta no singular X. Se prueba que el teorema de estabilidad, demostrado por el primer autor para los espacios de funciones racionales de CP^m a CPⁿ, se extiende a los espacios de morfismos continuos de CP^m a X, esencialmente con la misma demostración. En el caso de las curvas, nuestro resultado mejora las cotas conocidas para la dimensión de la estabilización.

Palabras clave: Variedad tórica, espacios de morfismos tóricos, Teorema de Stone-Weierstrass, resolución simplicial.

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