Open AccessOn n-th roots of meromorphic maps
Author(s) -
Juan Camilo García,
Rubén A. Hidalgo
Publication year - 2020
Publication title -
revista colombiana de matemáticas/revista colombiana de matematicas
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.176
H-Index - 7
eISSN - 2357-4100
pISSN - 0034-7426
DOI - 10.15446/recolma.v54n1.89789
Subject(s) - meromorphic function , mathematics , riemann surface , simple (philosophy) , riemann sphere , root (linguistics) , type (biology) , pure mathematics , combinatorics , surface (topology) , geometry , philosophy , linguistics , epistemology , ecology , biology
Let S be a connected Riemann surface and let φ: S → Ĉ bebranched covering map of nite type. If n ≥ 2,then we describe a simple geometrical necessary and sucient condition for the existence of some n-th root, that is, a meromorphic map ψ: S → Ĉ such that φ = ψn.