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The Gonality Of Riemann Surfaces Under Projections By Normal Coverings

Bujalance, E. and Etayo Gordejuela, J. Javier and Gamboa Mutuberria, Jose Manuel and 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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Abstract

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].

Item Type:Article
Uncontrolled Keywords:Mathematics, Applied; Mathematics
Subjects:Sciences > Mathematics > Functions
ID Code:15207
References:

E. Bujalance, J.J. Etayo, J.M. Gamboa, G. Gromadzki, Automorphism Groups of Compact Bordered Klein Surfaces, A Combinatorial Approach, in: Lecture Notes in Math., vol. 1439, Springer Verlag, 1990.

G. Castelnuovo, Ricerche de geometria sulle curve algebriche, Atti Acad. Sci. Torino 24 (1889) 346–373. (Memorie Scelte, Zanichelli Bologna, 1937, pp. 19–44).

H.M. Farkas, I. Kra, Riemann Surfaces, in: Graduate Text in Mathematics, Springer-Verlag, 1980.

G. Gromadzki, A. Weaver, A. Wootton, On gonality of Riemann surfaces. Geom. Dedicata (in press).

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).

Deposited On:16 May 2012 08:24
Last Modified:30 Nov 2012 09:06

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