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The Gonality Of Riemann Surfaces Under Projections By Normal Coverings


Bujalance, E. y Etayo Gordejuela, J. Javier y Gamboa, J. M. y Gromadzki, G. (2011) The Gonality Of Riemann Surfaces Under Projections By Normal Coverings. Journal Of Pure And Applied Algebra, 215 (5). pp. 983-988. ISSN 0022-4049

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A compact Riemann surface X of genus g ≥ 2 which can be realized as a q-fold, normal covering of a compact Riemann surface of genus p is said to be (q, p)-gonal.
In particular the notion of (2, p)-gonality coincides with p-hyperellipticity and (q, 0)-gonality coincides with ordinary q-gonality.
Here we completely determine the relationship between the
gonalities of X and Y for an N-fold normal covering X → Y between compact Riemann surfaces X and Y.
As a consequence we obtain classical results due to Maclachlan (1971) [5] and Martens (1977) [6].

Tipo de documento:Artículo
Palabras clave:Mathematics, Applied; Mathematics
Materias:Ciencias > Matemáticas > Funciones (Matemáticas)
Código ID:15207

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C. Maclachlan, Smooth coverings of hyperelliptic surfaces, Quart. J. Math. Oxford 22 (2) (1971) 117–123.

H.H. Martens, A remark on Abel’s Theorem and the mapping of linear series, Comment. Math. Helv. 52 (1977) 557–559.

F. Severi, Vorlesungen über algebraische Geometrie, Teubner, Leipzig (1921).

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Última Modificación:01 Mar 2016 16:27

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