Spaces of Morphisms From a Projective Space to a Toric Variety

Espacios de morfismos de un espacio proyectivo a una variedad tórica

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.

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.

Spaces of Morphisms From a Projective Space to a Toric Variety Espacios de morfismos de un espacio proyectivo a una variedad tórica JACOB MOSTOVOY¹, ERÉNDIRA MUNGUÍA-VILLANUEVA²

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

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Abstract

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.

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2000 Mathematics Subject Classification: 58D15, 32Q55.

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Resumen

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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Texto completo disponible en PDF

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References

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[18] J. Mostovoy, `Spaces of Rational Maps and the Stone-Weierstrass Theorem', Topology 45, (2006), 281-293.

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(Recibido en marzo de 2013. Aceptado en agosto de 2013)

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Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

@ARTICLE{RCMv48n1a03,
    AUTHOR  = {Mostovoy, Jacob and Munguía-Villanueva, Eréndira},
    TITLE   = {{Spaces of Morphisms From a Projective Space to a Toric Variety}},
    JOURNAL = {Revista Colombiana de Matemáticas},
    YEAR    = {2014},
    volume  = {48},
    number  = {1},
    pages   = {41--53}
}

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