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Revista Colombiana de Matemáticas
Print version ISSN 0034-7426
Rev.colomb.mat. vol.54 no.1 Bogotá Jan./June 2020
https://doi.org/10.15446/recolma.v54n1.89789
Original articles
On n-th roots of meromorphic maps
Sobre raíces n-ésimas de funciones meromorfas
1 Universidad Central del Ecuador, Quito, Ecuador
2 Universidad de La Frontera, Temuco, Chile
Let S be a connected Riemann surface and let φ: S → Ĉ be branched covering map of finite type. If n ≥ 2, then we describe a simple geometrical necessary and sufficient condition for the existence of some n-th root, that is, a meromorphic map ψ: S → Ĉ such that φ = ψ n .
Keywords: Riemann surfaces; holomorphic branched coverings; maps
Sea S una superficie de Riemann conexa y φ : S → Ĉ un cubrimiento ramificado holomorfo de tipo finito. Para cada n ≥ 2 describimos una condición geométrica necesaria y suficiente para la existencia de alguna raíz n-ésima, esto es, una función meromorfa ψ: S → Ĉ de manera que φ = ψ n .
Palabras clave: Superficies de Riemann; cubrimientos ramificados holomorfos; mapas
Acknowledgment.
We thank the anonymous referee for her/his comments and suggestions which contributed to improving this manuscript.
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Received: December 06, 2019; Accepted: April 01, 2020
This is an open-access article distributed under the terms of the Creative Commons Attribution License
